No, deadlifts DO work the lats
It's a very common assumption that the spinal erectors are responsible for extending the spine. However, that's not true.
You guys are right, it IS the lats that are the PRIMARY muscles that extend the back. The key is that you keep your back arched or at least neutral, which is accomplished by keeping your chest out and your head up.
If you do a dealift with a rounded back (which is possible, but dangerour for MOST people), there is naturally less involvement of the lats.
By the way, did you say you were using a ROWING MACHINE for lat development? If that's the case, what you may be feeling is the buildup of lactic acid in your biceps. Rowing machines are for anaerobic or aerobic stamina, not building strength.
If you're actually using a cable row with a weight stack, and your fatigue of the biceps is actually the limiting factor, then I suggest a couple of things, aside from the deadlifts already mentioned:
1) Do dumbell pullovers off an exercise bench or straight arm pulldowns with the lat machine bar (you can look up these exercises in any decent strength training book)
2) Strengthen your arm FLEXORS (that means the brachialis muscle, not the biceps neccessarily). Do hammer curls with a dumbbell for 4-6 reps, no more than twice a week. The biceps are responsible primarily for supination of the palm, while the brachialis is the muscle underneath that is actually responsible for arm flexion.
If you have a weak link, finding alternative exercises to bypass it is only good as a short-term solution. You will have to address the weak link itself eventually, and it will take some time.