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Medvedev does mean descent from someone who was called "bear", or for some reason reminded people of a bear. As a Jewish surname it is one of a multitude of "bear" names: Hebrew Dov, German-Yiddish Baer, Behr; Berkoff and Berkovitch with Slavic endings; Bernstein, Berenboim, etc., in ornamental form. What's going on with Jews and bears?
Lyashchuk must be Ukrainian. I imagine the basis of this name is Lyakh, which is another name for a Pole, cognate with Polish Lech. So the name probably means "little Pole", or "descendant of a Pole".