This is the fastest way I know of to get a Lair. You can start the upgrading process, by the time your Terran ally reasonablly has 0-1 marines, and that's if he does his Barracks at 7/10 instead of 10 or 11. Ready, well this is what you do. First, build 7 drones and send them all to the mineral patch. Then, when you have about 150 minerals, build a spawning pool. After that, when you have around 50 minerals, build an extractor. Build a few more drones until count is at 8/9. When extractor is ready, send 3 drones there. If you find you were late on building it, you can always send 4 to speed it up the collecting process. When you have about 150 minerals and 100 gas, start upgrading! And use this build in conjunction with muta rush or lurker rush, something that requires the gas. I was personally suprised when I found out that I could do it so quickily, just start the pool at 7, then extractor and Upgrade! Wow.

CreepColony's Opinion: I think fast lairs are best for lurker rush.