Try measuring from the end of the exterior wall. Try one way, then drive a nail. If it hits nothing, then try measuring from the other wall. You still have to drive nails, but two should hit a stud. The carpenters had to put their tape on one end or the other when they laid out the wall. The way I look at it, you got a 50% chance.
One more thing, you mentioned using 5½ long lag bolts, but not the diameter. If they are 3/8 or ½ you probably should drill holes for them first. Wedging a bolt that big into a 2x4 stud that is 1½ inches wide may split the stud. If that happens you could not only lose precious grip on the lag bolt, but seperate drywall sheets inside and risk popping screws or nails in the drywall as well. Drilling holes would be great insurance. It would:
Make sure you are hitting something very solid
Prevent studs from splitting
I am just stating my opinion and trying to help you reduce some work for yourself...I am in no way trying to be a know it all.
I have no intention of traveling from birth to the grave in a manicured and well preserved body; but rather I will skid in sideways, totally beat up, completely worn out, utterly exhausted and jump off my tractor and loudly yell, "Wow, this is what it took to feed a nation!"