Blades academy product Lowton has put pen to paper on a four-year contract which will keep him at Villa until the summer of 2016.
Lambert said: "Matthew is a really talented young player who brings a lot of things that can really benefit the club.
"He's a good player already and he's only young so he has the potential to be a really good player for us.
"He's hungry to succeed and to go further in the game, both of which are attributes that we want at this football club and that we are looking for.
"We won't put any pressure on him, we just want him to go out and enjoy playing.
"What he's done so far at Sheffield United has been great so hopefully we can progress him a bit and he'll do very well for us."