Yes it would, ...probably.
A lich Rejuvenation ability is triggered when the lich is destroyed. The petrification condition states that a petrified creature is incapacitated and transformed to stone, but not destroyed. So, if you manage to petrify a lich, it will become a statue and until it is de-stoned... or someone smashes it into pieces. A petrified lich is a really resilient statue, retaining all the lich damage inmunities and hit points and gaining resistance to all damage to boot, but it can still be destroyed with magic weapons, spells, acid, etc. All it takes is one or more well prepared minions infiltrating your garden at nigth to destroy the lich, enabling it to use its trademark escape clause and return later to enact a carefully planned revenge. Be sure to keep the statue well-watched and take advantage of the lich state to find and destroy its phylactery.
Also, if the lich happens to have the phylactery on its person when petrified (not very probable), the item will become lodged into the stone (being a magic item spares it from petrification) and you'll have an interesting choice: Leave it as it is, and hope that nobody breaks the statue, or try to extract the phylactery from the statue without breaking it yourself. If you choose the later and worst come to worst, you will have 1D10 days to find a way to destroy the phylactery (not an easy task) or to prepare for a rematch with a angry lich after its new body reforms next to the phylactery.