A short ride on the Brown Line to the Wellington stop will take you to
Fish Bar. They have a one pound lobster roll (I assume it's made from a one pound lobster, not a one pound roll) for $22, so I know you said you would prefer not a roll, but that's a fair amount of lobster. I haven't had the lobster roll there, but I ate there just a month ago and everything I had (grilled octopus, artichoke fritters) was excellent.
Glenn's Diner is another possibility, although I haven't been there in forever. They have a lobster roll on the menu, too, for $18. It's at the Montrose stop on the Brown Line, or you could just walk. Again, I know you said you would prefer not a roll, but this is the only place mentioned so far that meets your criterion of being within a mile walk of Lincoln Square.
If you're going to take the el or drive anyway and you'd consider re-thinking not wanting to go as far as Evanston, it's worth noting that
Davis Street Fishmarket is running a special this summer, with a whole pound-and-a-quarter lobster dinner for $19.95.