YES! In your Manager's Center, there are links to view each lineup you have. In normal leagues and non-DH theme leagues, only vs. LHP and vs. RHP are available. In DH theme leagues, only vs. LHP w/DH and vs. RHP w/DH are available. For theme leagues where only one leagues uses the DH, all 4 lineup types are available. One of the lineups will be loaded up already. If you want to switch lineups, just click on that link to load it for editing.
When you click on 'Save Batting Order', you will be saving the batting order for the current lineup.
After saving a lineup, you can click on Copy to Opposite to copy the current lineup to the lineup against the opposite handed pitcher. Ex. If you are looking at your vs. RHP lineup and click Copy To Opposite, it will take your settings and copy them to the vs. LHP lineup. This works the same way no matter what type of league you are using.
In theme leagues where only one league uses the DH, there is a button to copy the lineup to all other lineups. If you click this, the current lineup you are looking at will be copied to all 3 other lineups while inserting or removing a player if necessary. Ex. If you are looking at your vs. RHP lineup and click Copy To All Lineups, it will take your settings and copy them to the vs. LHP, vs. LHP w/DH and vs. RHP w/DH lineups while inserting the best hitter by OPS in as the DH in the DH lineups. If you are copying from a DH lineup, it just removes the DH for the non-DH lineups.