My daughter was heavily involved in theater at Purdue. It seemed like 90% of the theater kids were engineers, and there were many different levels of performance groups, from the high involvement to the low. My sense is that it’s not going to be necessary for your son to double major to still stay very involved in technical theater.
My D’s last bf was an IT guy but did all the lighting and tech for his local community theater as a side gig.
That said, I believe you can double major in EE and lighting design and tech at UIUC.
Another program to look into is Northwestern. They have an MFA degree in lighting and tech but there are a host of related undergraduate offerings and the quarter system lends itself to taking classes outside of one’s primary major.