Rye grass is usually used as part of a hardwearing lawn. Mow regularly to desired height.
I don't know about suitable for lawns. I have used it for reseeding a cow paddock, mixed with other grasses. It grows fast and tall but only lasts about 3 years. Farmers use it as a catch crop.
Sowed it as a lifter with Vicia sativa (sinker and fixer). Nothing! I sowed it too late, the ground was too heavy or the wood mice ate it.
It's usually for overwintering or agi use. When were you planning to dig it in?
Strange, not an ornamental grass for a container. You'd do better with something like a pennisetum.
It. rye grass in pic.