Walking on the lawn in this park is prohibited.
Your lawn of life is just your lawn. Of course it's alive, otherwise it wouldn't be a very good lawn.
The reading for 芝 is the one you learned with the kanji. The reading for 生 is one you haven't seen before (exception). It's ふ, and you can remember it by thinking how you were such a fool (ふ) for putting all that poison on it. Now it's dying, and now it's becoming less of a lawn.