diff --git a/pyproject.toml b/pyproject.toml
index 51781d4953935..1e2c59d28a3db 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -89,7 +89,6 @@ module = [
     "pytorch_lightning.trainer.supporters",
     "pytorch_lightning.trainer.trainer",
     "pytorch_lightning.tuner.batch_size_scaling",
-    "pytorch_lightning.tuner.lr_finder",
     "pytorch_lightning.tuner.tuning",
     "pytorch_lightning.utilities.auto_restart",
     "pytorch_lightning.utilities.data",
diff --git a/src/pytorch_lightning/tuner/lr_finder.py b/src/pytorch_lightning/tuner/lr_finder.py
index ad15707d079f1..9e584708f369e 100644
--- a/src/pytorch_lightning/tuner/lr_finder.py
+++ b/src/pytorch_lightning/tuner/lr_finder.py
@@ -16,7 +16,7 @@
 import os
 import uuid
 from functools import wraps
-from typing import Any, Dict, Optional, Sequence
+from typing import Any, Callable, cast, Dict, List, Optional, Sequence, TYPE_CHECKING, Union
 
 import numpy as np
 import torch
@@ -27,9 +27,10 @@
 from pytorch_lightning.core.optimizer import _init_optimizers_and_lr_schedulers, _set_scheduler_opt_idx
 from pytorch_lightning.loggers.logger import DummyLogger
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
+from pytorch_lightning.utilities.imports import _RequirementAvailable
 from pytorch_lightning.utilities.parsing import lightning_hasattr, lightning_setattr
 from pytorch_lightning.utilities.rank_zero import rank_zero_warn
-from pytorch_lightning.utilities.types import LRSchedulerConfig
+from pytorch_lightning.utilities.types import LRSchedulerConfig, STEP_OUTPUT
 
 # check if ipywidgets is installed before importing tqdm.auto
 # to ensure it won't fail and a progress bar is displayed
@@ -38,6 +39,10 @@
 else:
     from tqdm import tqdm
 
+_MATPLOTLIB_AVAILABLE: bool = _RequirementAvailable("matplotlib")  # type: ignore[assignment]
+if _MATPLOTLIB_AVAILABLE and TYPE_CHECKING:
+    import matplotlib.pyplot as plt
+
 log = logging.getLogger(__name__)
 
 
@@ -95,16 +100,16 @@ def __init__(self, mode: str, lr_min: float, lr_max: float, num_training: int):
         self.lr_max = lr_max
         self.num_training = num_training
 
-        self.results = {}
+        self.results: Dict[str, Any] = {}
         self._total_batch_idx = 0  # for debug purpose
 
-    def _exchange_scheduler(self, trainer: "pl.Trainer", model: "pl.LightningModule"):
+    def _exchange_scheduler(self, trainer: "pl.Trainer", model: "pl.LightningModule") -> Callable[["pl.Trainer"], None]:
         """Decorate `trainer.strategy.setup_optimizers` method such that it sets the user's originally specified
         optimizer together with a new scheduler that takes care of the learning rate search."""
         setup_optimizers = trainer.strategy.setup_optimizers
 
         @wraps(setup_optimizers)
-        def func(trainer):
+        def func(trainer: "pl.Trainer") -> None:
             # Decide the structure of the output from _init_optimizers_and_lr_schedulers
             optimizers, _, _ = _init_optimizers_and_lr_schedulers(trainer.lightning_module)
 
@@ -123,6 +128,7 @@ def func(trainer):
 
             args = (optimizer, self.lr_max, self.num_training)
             scheduler = _LinearLR(*args) if self.mode == "linear" else _ExponentialLR(*args)
+            scheduler = cast(pl.utilities.types._LRScheduler, scheduler)
 
             trainer.strategy.optimizers = [optimizer]
             trainer.strategy.lr_scheduler_configs = [LRSchedulerConfig(scheduler, interval="step", opt_idx=0)]
@@ -131,13 +137,18 @@ def func(trainer):
 
         return func
 
-    def plot(self, suggest: bool = False, show: bool = False):
+    def plot(self, suggest: bool = False, show: bool = False) -> Optional["plt.Figure"]:
         """Plot results from lr_find run
         Args:
             suggest: if True, will mark suggested lr to use with a red point
 
             show: if True, will show figure
         """
+        if not _MATPLOTLIB_AVAILABLE:
+            raise MisconfigurationException(
+                "To use the `plot` method, you must have Matplotlib installed."
+                " Install it by running `pip install -U matplotlib`."
+            )
         import matplotlib.pyplot as plt
 
         lrs = self.results["lr"]
@@ -162,7 +173,7 @@ def plot(self, suggest: bool = False, show: bool = False):
 
         return fig
 
-    def suggestion(self, skip_begin: int = 10, skip_end: int = 1):
+    def suggestion(self, skip_begin: int = 10, skip_end: int = 1) -> Optional[float]:
         """This will propose a suggestion for choice of initial learning rate as the point with the steepest
         negative gradient.
 
@@ -196,7 +207,7 @@ def lr_find(
     """See :meth:`~pytorch_lightning.tuner.tuning.Tuner.lr_find`"""
     if trainer.fast_dev_run:
         rank_zero_warn("Skipping learning rate finder since fast_dev_run is enabled.")
-        return
+        return None
 
     # Determine lr attr
     if update_attr:
@@ -218,7 +229,7 @@ def lr_find(
         trainer.progress_bar_callback.disable()
 
     # Configure optimizer and scheduler
-    trainer.strategy.setup_optimizers = lr_finder._exchange_scheduler(trainer, model)
+    trainer.strategy.setup_optimizers = lr_finder._exchange_scheduler(trainer, model)  # type: ignore[assignment]
 
     # Fit, lr & loss logged in callback
     trainer.tuner._run(model)
@@ -304,14 +315,16 @@ def __init__(
         self.num_training = num_training
         self.early_stop_threshold = early_stop_threshold
         self.beta = beta
-        self.losses = []
-        self.lrs = []
+        self.losses: List[float] = []
+        self.lrs: List[float] = []
         self.avg_loss = 0.0
         self.best_loss = 0.0
         self.progress_bar_refresh_rate = progress_bar_refresh_rate
         self.progress_bar = None
 
-    def on_train_batch_start(self, trainer, pl_module, batch, batch_idx):
+    def on_train_batch_start(
+        self, trainer: "pl.Trainer", pl_module: "pl.LightningModule", batch: Any, batch_idx: int
+    ) -> None:
         """Called before each training batch, logs the lr that will be used."""
         if (trainer.fit_loop.batch_idx + 1) % trainer.accumulate_grad_batches != 0:
             return
@@ -319,9 +332,11 @@ def on_train_batch_start(self, trainer, pl_module, batch, batch_idx):
         if self.progress_bar_refresh_rate and self.progress_bar is None:
             self.progress_bar = tqdm(desc="Finding best initial lr", total=self.num_training)
 
-        self.lrs.append(trainer.lr_scheduler_configs[0].scheduler.lr[0])
+        self.lrs.append(trainer.lr_scheduler_configs[0].scheduler.lr[0])  # type: ignore[union-attr]
 
-    def on_train_batch_end(self, trainer, pl_module, outputs, batch, batch_idx):
+    def on_train_batch_end(
+        self, trainer: "pl.Trainer", pl_module: "pl.LightningModule", outputs: STEP_OUTPUT, batch: Any, batch_idx: int
+    ) -> None:
         """Called when the training batch ends, logs the calculated loss."""
         if (trainer.fit_loop.batch_idx + 1) % trainer.accumulate_grad_batches != 0:
             return
@@ -372,7 +387,7 @@ def __init__(self, optimizer: torch.optim.Optimizer, end_lr: float, num_iter: in
         self.num_iter = num_iter
         super().__init__(optimizer, last_epoch)
 
-    def get_lr(self):
+    def get_lr(self) -> List[float]:  # type: ignore[override]
         curr_iter = self.last_epoch + 1
         r = curr_iter / self.num_iter
 
@@ -384,7 +399,7 @@ def get_lr(self):
         return val
 
     @property
-    def lr(self):
+    def lr(self) -> Union[float, List[float]]:
         return self._lr
 
 
@@ -410,7 +425,7 @@ def __init__(self, optimizer: torch.optim.Optimizer, end_lr: float, num_iter: in
         self.num_iter = num_iter
         super().__init__(optimizer, last_epoch)
 
-    def get_lr(self):
+    def get_lr(self) -> List[float]:  # type: ignore[override]
         curr_iter = self.last_epoch + 1
         r = curr_iter / self.num_iter
 
@@ -422,5 +437,5 @@ def get_lr(self):
         return val
 
     @property
-    def lr(self):
+    def lr(self) -> Union[float, List[float]]:
         return self._lr