1. It spreads by underground runners, so your edging would have to be deep enough to prevent that.

2. You can use mulch while it's filling in, and it won't slow the spread.

3. You don't usually have to fertilize it, at all.

PS...It's not really a grass, but a flowering perennial. You might get more help if you post to the Perennial Forum.

My monkey grass does not flower...the blades are 3-4 inches long. My problem is that although I have watered every day during our hot Dallas summer, much of the grass is brown and sparse. Can fertilizer or dirt help it? please advise.
Thanks,
Nete

Try aluminum gutter material in various colors for brick edging.
After years of maintaining angled brick edging around our front beds, I relaid the upright angled brick within aluminum gutter material which holds the brick in a straight line and keeps our St. Augustine grass from growing into it. After three years, we still love this maintenance-free approach.

It might be helpful to identify exactly what we are talking about here as there seems to be a couple of different posters with questions. Monkey grass is a common name applied to both Liriope and Ophiopogon (mondo grass, lilyturf, aztec grass, etc.). Neither are native to the US and the chances of finding either growing naturally and unattended along the side of a country road are a bit slim :-) And neither is a grass - both are fleshy rooted, rhizomatous perennials of the Lily family generally used as groundcovers. They both produce noticeable flowers although some forms (dwarf mondo, Ophiopogon japonicus 'Nana') seldom bloom. Care for both of these types of plants is somewhat different than that involved with a true ornamental grass, which is why clarification of what we are really talking about is requested.