Vinca runs wild through grass, forest, everywhere. It's very invasive and hard to eradicate by digging or poisoning.

My experience is that it crawls into the lawn without pausing, even with a brick barrier above ground and edging below. I have been removing mine.

My advice is to choose another ground cover. Lamium is great and although it can be invasive, it is very easy to pull out what you don't want.

Actually, there is a really mannerly and charming white vinca minor 'Gertrude Jekyll' which has the virtue of being both floriferous and reticent....not a lawn smotherer......but not totally without some attempts at takeover. A nifty lawnmower usually puts paid to world domination attempts.