Lex Luthor is required in all matches of challenge battle 2. As usual, challenge battle 2 is by far the easiest out of the three battles (2, 4, 5) that do not restrict character tier, with the weakest opponents.
If you don't have any version of Lex Luthor, there is no need to dish out big money for Lex Luthor/Krypto at this point - just get the bronze Lex Luthor/Prime or the silver Lex Luthor/Insurgency, both of which has useful team buffs that would make bronze or bronze/silver only battles (1 and 3) much easier.
Challenge: Power Surge!
Challenge: Countdown! (You have 3 minutes to defeat your opponents)
Challenge: Dampening Field!
This match awards 3 energy cards.