Is there a town named Lincoln in every state?

Possibly, just like there is a Lexington and a Springfield in every state too

No Springfield does not exist in every state, not in Hawaii and others. I believe Springfield is in 36 states. Neither is Lexington nor Lincoln a town name in every state.

My research has shown that Middletown or Middleton is that most popular town name, appearing in 46 states. In second place, Centerville in 45 states.