I don't know how big you are, or what wetsuit you used, but assuming you were properly weighted here is some data from the spreadsheet mentioned above, that suggests you didn't need your lift bag at all. This is properly an advanced topic, but you have raised the issue, so I'll discuss it:
A 5'10" 175# muscular diver wearing a 5 mm wetsuit and hood with the worst 120CuFt steel tank for buoyancy (-7 lb empty) might require 6# weight as you did, to be neutrally buoyant.
His wetsuit, which provided about 21# of lift on the surface, is compressed at 80 ft so it now only provides 7# of buoyancy.
Thus, at the beginning of the dive, carrying almost 10# of air, with a bcd failure, he is over 17# negatively buoyant. Thus, your observation is correct: a bcd failure is a struggle. A buddy could help; a lift bag could help; and partial weight ditching could help.
If this diver ditched 4# out of his total 6# carried lead at that moment, he would be only 13# negative, which is a manageable negative buoyancy to fin up for a short while. As he rose, his wetsuit would expand, and things would get easier. With this new weighting, he would arrive at the surface only 0.4lb negatively buoyant, and could ditch his rig at that point.
If this emergency arose halfway through the dive, the diver is only 12# negative, because he has consumed 5# of air. Ditching 2#, he can swim up 10# briefly, until wetsuit expansion takes over. He is then neutral at 12 feet (0# buoyant), and can do a normal safety stop. Continuing up, he arrives 2.7# positive, and can ditch the other 2# and rest, awaiting pickup.
Or his buddy could have helped him. Or he could have used a lift bag for the first 60 feet or so, and then released it.
No, you don't need a drysuit. But you do need to plan, and MOST IMPORTANT, you need to be properly weighted. If you are overweighted, on top of what you have described, you are placing yourself needlessly at risk.
Dive Safe!
