Pet rabbits eating grass are usually those that are set outside in a safe run/area on grass that the owner knows to be free of pesticides, fertilizer and weed control. The rabbit grazes on the lawn and gets grass that way. If one is going to allow a rabbit to eat grass, they should do so gradually at first because fresh green grass would be considered a diet change.
Those that are allergic to timothy hay often do just fine with orchard grass hay. You might want to try orchard hay.