Honestly, you make a good point. Our LHP reliever depth is basicaly non-existent. There's Pannone, potentially Borucki if he doesn't break the rotation, ditto Anthony Kay, Brian Moran, and Bergen. It's pretty gross and I have to imagine Bergen will have consideration. In the minors we had Kirby Snead and Jake Fishman, but neither is on the 60 player pool.
It should also be noted that LOOGYs are basically a thing of the past under the new rules, so you better hope your lefties are good enough to expose to RHH in case they don't get out their assigned 2-out lefty.