How to use GridSearchCV for learning rate optimisation (Keras LSTM)

Question

I am tuning Keras Sequential model and have the capability of doing epochs, batch_size, but I'm unsure how to test multiple learning rates, different learners, and different LSTM units. Below is my code:

def build_model():
model = Sequential()

model.add(LSTM(50, input_shape=(5,5),activation = "relu")) #return false
model.add(Dropout(0.2))
          
model.add(Dense(1,activation = "linear"))

model.compile(loss='mse',optimizer="Adam", metrics=["mse"])  
return model

Which needs the KerasRegressor to allow the cross validations

model = KerasRegressor(build_fn= build_model,batch_size = 256, verbose = 1)

Then defining the grid search as

param_grid = dict(epochs = [10,20,30])
grid = GridSearchCV(estimator = model, param_grid = param_grid, n_jobs = -1 , cv = 5)
grid_result = grid.fit(X_train,y_train)
print("Best: %f using %s" % (grid_result.best_score_, grid_result.best_params_))
means = grid_result.cv_results_['mean_test_score']
stds = grid_result.cv_results_['std_test_score']
params = grid_result.cv_results_['params']
for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

Note* I have only tested the epochs for a trial, but my main aim is to test learning rates in the param grid, aswell as other varying hyperparameters