Interesting!
This is what I see from the .h5 model:

Screenshot 2021-12-05 at 16.07.06992×648 11.7 KB

and this is after conversion:

Screenshot 2021-12-05 at 16.07.381336×1168 101 KB

Let me ping @khanhlvg  to see if he can sed some light here.
Code:
data = np.array([[0.195312, 0.05913, 0.089844, 0.550781, 0.320312]])
normalizer = tf.keras.layers.Normalization(axis=-1)
normalizer.adapt(data)
lr_model = tf.keras.Sequential([
    normalizer,
    tf.keras.layers.Dense(units=3, activation='sigmoid')
])
lr_model.load_weights("linear_regression.h5")
target_y = lr_model.predict(data)
print(target_y)

# Convert the model.
converter = tf.lite.TFLiteConverter.from_keras_model(lr_model)
tflite_model = converter.convert()

# Save the model.
with open('model.tflite', 'wb') as f:
  f.write(tflite_model)

TensorFlow version 2.7.0
Best