Generally speaking venture capitalists fund companies that can either be acquired for a substantial sum, or that can go public. I don't know of any law firms that have gone public, nor law firms that have been funded by VC's.
There are investors in other industries who would not have "go public" as a condition, although they may not be VCs per-se. Law firms can be acquired for significant amounts though and they're usually very profitable, so there's an opportunity, but unlike technology/sciences/product development/retail it's really hard to weigh up the factors surrounding a law firm to establish the risk.
I don't know of any law firms that have gone public
It's pretty much unheard of (the first went public in 2007 - http://is.gd/cDks). There are lots of potential issues, such as loyalty to shareholders affecting attorney-client privilege. There are laws in the UK and US regarding this too. Don't quote me on this, but commonly non-lawyers cannot own shares in law firms in the US.