Lunch in Lodi?
Not a hamburger dive, but Wine and Roses Restaurant is excellent! They are located adjacent to the Lodi Visitor's Center where you could go and wine taste and pick up information on the area. Our pourer was very informative about the area, they produce some amazing Old Vine Zins in Lodi. :)
Altho it's my stomping grounds, I very seldom eat lunch in Lodi, so I can't tell you who does a particular good job of the mid-day meal. As for burgers, if you're willing to drive 20 minutes or so, the Squeeze Inn in Galt does a really good cheeseburger, made famous by Guy Fieri on "Diners, Drive-ins and Dives" (albeit at the Sacramento location). If you go, bear in mind that there's some interchange work being done in Galt, so the best way to get there is to drive past the normal exit and get off Highway 99 at Twin Cities Road, cross over to the west frontage, then head south about two miles to Pringle Avenue.
Alternately, Bob's at the Marina in Stockton (about a 10 minute drive in the other direction) used to have a pretty good burger, too, but it's been at least five years since I had one, so I don't know if they're still any good. Also in Stockton is Flip's, on Waterloo Road at Filbert Street. Crummy neighborhood, but it'll be safe during the day.
My wife and I both enjoyed our burgers at Andre’s Café a couple years ago. They are not gourmet, but they were tasty. This may qualify as a dive.
We also like the soup & sandwich lunch at Phillips Farm Café at the Michael David Winery on Hwy 12 near I-5.