Without getting on a soapbox about America's number one cultivated crop, I will just say that as a new homeowner I would like to get rid of as much lawn as possible from my front and back yards. I found this really pretty flower growing in the side lawn area and it appears to be some kind of ground cover, though I don't know if the previous owner planted it or it is native. What is it and how can I encourage it to replace my current grass?
That's Creeping Charlie, an extremely invasive groundcover that is considered a noxious weed in many states. It's actually not very good at preventing weed growth (the primary reason for a groundcover, IMO) because its growth is too open and fails to keep weed seeds from hitting the ground; it also doesn't prevent sunlight from hitting the ground.
Encouraging this to grow is a very bad idea. If you live in an urban area, your neighbors will not be thrilled with you because this stuff spreads like crazy.
There are many other options for groundcovers that are much less nasty:
- Creeping Thyme (there are many cultivars)
- Mazus reptans (for shade and part-shade)
- Creeping veronica (many cultivars)
- White clover. This is also considered a weed by many people, although it's an excellent pollinator plant when in bloom and enriches the soil
- Some sedges (Carex species). If you don't want it to be necessarily walkable, I recommend a sedge called Carex pensylvanica - it spreads fairly quickly and has a grass-like look.
There are many other options for you. In all cases, groundcovers (including lawn grass) will enter any flower or vegetable beds, so edging or maintenance is a must.
If you want something low and moderately walkable, I suggest woolly thyme.