Etymology of 「芝生」 and pronunciation of 「生」 here

生 with a reading of ふ is uncommon, but it's not only in 芝生【しばふ】. It was used in Old Japanese as a standalone noun, with a general sense of "place with lush greenery". Given the sense and reading, I suspect it might be connected somehow to the verb forms 生【は】える ("to grow", intransitive) and 生【は】やす ("to grow something, to make something grow", transitive).

In more recent years, this 生【ふ】 isn't used on its own, and appears mostly as the second element in various compounds.

Here's a quick-and-dirty survey of my electronic Daijirin copy for all the words ending in 生【ふ】:

• 粟生【あわふ】, "millet field" (archaic)
• 切生【きりふ】, "a type of goose feather with thick black bands" (the 生 here is probably ateji for 斑【ふ】)
• 草生【くさふ】, "place with a lot of grass growing"
• 笹生【ささふ】, "place with a lot of sasa (dwarf bamboo) growing"
• 芝生【しばふ】, "lawn"
• 杉生【すぎう】, (older すぎふ), "place with a lot of cedars growing" (archaic)
• 芹生【せりょう】, (older せりふ), "place with a lot of seri (Japanese parsley) growing"
• 園生【そのう】, (older そのふ), "cultivated garden"
• 武生【たけふ】, place name for a city in Fukui Prefecture, from 竹【たけ】 + 生【ふ】, "place with a lot of bamboo growing"
• 茅生【ちふ】, "place with a lot of thatch growing" (archaic)
• 麦生【むぎふ】, "place with a lot of grass-grain (wheat, oat, barley) growing"
• 葎生【むぐらふ】, "place with a lot of mugura (creepers, vines) growing" (archaic)