#You can cast the spell
I previously had a much more complicated answer here that I have saved in case it is actually important but I beleive your question can be answered by looking at the optional rule for simultaneous effects.
Xanathar's Guide to Everything (p. 77) offers the following rule regarding simultaneous effects:
If two or more things happen at the same time on a character or monster's turn, the person at the game table – whether player or GM – who controls that creature decides the order in which those things happen.
The wave of lethargy occurs at the same time as you are casting the second spell. As such you can choose to have the spell be cast first and then the lethargy take effect after.