YES. You can change position by taking the player in the lineup and replacing them with a bench player, then replacing the bench player with the player you want.
For example: In the scrambled lineup, Arod is catching and Posada is at third base. Joe Scrub is called up from the minors and is on the bench. The way you get Arod to third and Posada to catcher is to replace Arod at catcher with Joe Scrub, then replace Posada at third with Arod, then replace Joe Scrub at catcher with Posada. So its a bit like three card monte, shuffling the positions around.
Don't forget you have FOUR lineups to correct (LH w/DH, LH w/o DH, etc. )