What value(s) of capacitor prevented the lights from flickering before the cap ultimately failed? I would use a similar value to what worked before.
4μF has a reactance of -j 663 ohms at 60Hz and so it will be drawing about 0.18 amps of reactive current with 120VAC across it, which is not all...
Here's another capacitor that should be more suitable for your application than a motor running capacitor:
https://www.mouser.com/ProductDetail/EPCOS-TDK/B33331V7405J080?qs=%2Fha2pyFadujzqlauzP%252BWPCYIRjxUd77Jm9NTjMobfp8EXFixTnckIg%3D%3D...
