I think Conor beats him. Lawler will have the size advantage but size isn't everything. It only takes so much to KO somebody and if you land in the right spot at the right time, you can put down practically anybody.
Lawler has gotten wobbled pretty good in basically every fight for the last few years. If I remember correctly, was hurt by Hendricks in the first, hurt BADLY by Rory, wobbled by Brown in the 1st, wobbled by Ellenberger (I could be wrong about this one), and Condit also hurt him, too. Lawler arguably lost to Hendricks twice, was losing to Rory until he got the knockout, etc, etc.
I think Conor catches him eventually. Lawler is a little too sloppy for Conor's extremely powerful, quick and precise striking. Not saying Conor WOULD beat him, but I would definitely pick him if they were to fight. We've seen much smaller fighters completely destroy much bigger opponents. Anything can happen. Conor can beat anybody between 145-170, in my opinion. He has the skills to do it. He's one of the best strikers in MMA history, that's a fact.