I was wondering if the storm titan is a requirement to be beaten to get into lemuria, or if it would be the catacombs quest line that would be required.
Lemuria is after Karamelle, and you need to beat the storm titan to get to Karamelle, so by the transitive property one can deduce you must defeat the storm titan to get to Lemuria. Catacombs is side content, so not required, although recommended.
The Storm Titan is the requirement. Wizard101 runs on a storyline format, so you need to first finish Empyrea (the Storm Titan), and do Karamelle (the world after Empyrea) to get to the next world (Lemuria).
Grizzleheim, The Catacombs, Aquila, and Wysteria, for example, are not part of the main storyline. They do not need to be completed to progress in the main storyline. But Empyrea is.