What's a good strategy to kill the Brutalisk with lava in The Devil's Playground?

I've tried to lure him into the lava with my reapers with 30 seconds before the next flow, but he always scampers back to his little corner right before it comes up. What's the best way to kill him with lava?

I built supply depots at the bottom of the ramp, and made them sink into the ground. Then I created a line of marines for him to kill, like a cookie trail for him to follow, then told them all to "stop" (so they wouldn't move). With about 50 seconds left, I sent a single reaper to lure the brutalisk to my cookie-trail of marines. When he got below the ramp, I put the supply depots back up.

The lava doesn't kill him right away, but the marines damaged him enough that he died before he could make it back.

It took me a while to figure this out, but when I did it was pretty easy. My solution is a variation of the bunker trick mentioned in another answer.

First of all, kill the other units around the brutalisk. This shouldn't be too hard, and you don't want them getting in your way.

Float a command center (with SCV's loaded in it) down to the expansion just to the right of the brutalisk. You could just run some SCVs there, but the CC makes this solution a little more elegant. Using this back entrance is better than the front entrance is better because you don't have to lure the brutalisk for as great a distance.

Build a bunker in the expansion, and use a marine to lure the brutalisk to the bunker. You don't have to worry about the timing too much, because you can use SCVs to repair the bunker, effectively keeping the brutalisk tied up indefinitely. (Just use a single marine, because you don't want to accidentally kill the brutalisk.)

Just before the lava rises, have the CC load up the SCVs and lift off. You'll lose the bunker and one marine, but everything else will survive. And as a bonus, you have your next base to mine from!