Supplies won't hinder Russia to invade Lviv.
Morale and coordinated action of the Ukrainian army are needed for that. Remember that the Ukrainian army is rather young. They started mobilization this week. Russia has years of fighting experience, not alone from Syria. I certainly sympathize with Ukraine, but I am not convinced that they can stop the massively stronger aggressor.
Edit: Russian troops are not very efficient and morale might be questionable in some parts. But Putin does not care how many of them die. He has hundreds of thousands more.