How long can a lamb shoulder sit out on the counter?

Use your instant read thermometer and when it is about 65F it is time put it in the oven.

If the shoulder is one whole piece, I don't think 2 hours on the counter is too long, unless the room temp is on the warmer side (> 75degrees F). If it's ground meat, then, yes, 2 hours is too long.

J. Kenji López of SeriousEats.com did an experiment (using steak) where he tested if allowing it to come to room temperature made any difference. After two hours a 15 oz steak had gone from 38F to 49.6F. That's a (compared to lamb shoulder) thin piece of meat that didn't get anywhere close to a normal room temperature in two hours. Upon cooking the steaks, there was no difference between the piece from the fridge and 'room temperature' piece.

So long as it's not frozen in the middle, I would have no problem slinging it straight from fridge to oven. Then again, rather than brining (which I find pointless and wasteful) I'd have salt rubbed it and left it uncovered in the fridge to dry the surface out and thus get a better Maillard on it.

If you're unwilling to go fridge to oven in one fell swoop, and want to leave the shoulder out, it might be interesting to check with a probe thermometer the temperature of the shoulder (in the centre of the thickest part) when it gets out of the fridge, after an hour, and just before it goes in the oven. After all, all I've write above is from an experiment conducted upon a steak. The shoulder bone could make a difference.

I think 2 hours is just right.