Yes, Quilava is able to learn Strength.
First, you have to get the HM strength, then teach it to and a Pokemon and you can move boulders.
Strength
To move boulders in Pokemon Gold you need a Pokemon with the HM move Strength. Selecting the Pokemon in the menu outside of battle should let you use it if you have beaten the Olivine City Gym.
you mest get the hm strength.
Use the HM move Strength.
With the HM move strength.
Quilava is a Fire type pokemon.
use strength
You get the hm strength and give it to one of your pokemon
move the boulders to where the lake Pokemon are
Move the boulders around the place where the lake Pokemon are.
make one of your pokemon learn the hm strength