I'd put Flair ahead by a slim margin. Correct me if I'm wrong because I'm not exactly an 80's historian, but did Lawler ever hold the NWA World title? I know he held a ridiculous amount of titles but ever the World strap?
No, and if you are interested in why with a healthy dose of wrestling history read on.
In 1977 Lawler was wrestling for the NWA Mid-America (which covered parts of about 6 states) territory for Nick Gulas. He got some shots at Brisco, and Race, and Gulas was working on getting his young star a title run. The Lawler NWA title chase angles drew big business. Gulas would bring in guys like Dick the Brusier, Wrestling 2, Mil Mascaras, Bobo Brazil, and Funk billing it as a "winner gets a title shot match". Lawler looked like he was destined for at least a short run. Eventually there was a rift between Gulas and his young booker Jerry Jarrett. Jarrett, Lawler, and other stars hated putting over Nick's son George, and main events with George made less money in the lucrative western (Memphis) end of the territory.
Jarrett split on his own and offered Lawler part of the ownership if he would come with him. Many of the other stars went with them. The territory split in two (The CWA was born). Since the NWA sided with Gulas and sent in stars for the battle, Jarrett reached out to the AWA since Lawler's NWA title shots were such a huge draw he needed something for Lawler to chase. He simply repeated the same angle but Lawler was chasing the AWA title.
A lot of wrestling fans do not remember this era, but at that time the AWA title was considered the second world title and on equal footing as the NWA belt, it was not until probably 80 that the WWF was considered the third world title. So the AWA title really mattered, and their world champ was held in just as high, sometimes higher esteem than the NWA champ and certainly the WWWF champ.
Anyways, Verne was notorius for only wanting to keep the belt on Bockwinkle. Every time Jarret would think he had worked out a deal for a Lawler AWA title run Gagne would back out at the last minute. This caused Jarrett to flirt with the NWA again, (Flair appeared on television once) since Gulas went out of business shortly after the split. However the AWA association put Lawler on the NWA's backburner, and Fritz, Dusty, and the Crocketts were not going to let Lawler jump their boys in line.
Finally in 1988 as the AWA fortunes were fading and as a last gasp Gagne reached out to Jarrett. The CWA was one of the few territories that was still doing decent business during the WWF takover. Lawler held the title and in fact unified it with the World Class title as well after beating Von Erich (World Class had pulled out of the NWA by then as well).
Lawler was the last "legit" AWA champ. After a dispute between Jarrett, Lawler and Gagne, Verne stripped Lawler and watched his company fade away, ending the AWA's tenure as one of the three "World" promotions.
In the end it was the split that probably cost Lawler at least one NWA run. The NWA was not above letting local promotions have a brief title run (Tommy Rich, Kerry Von Erich) for a payoff.