Yes the city can require you to be licensed. Very standard.
They can and they do. Especially Lake Worth. Hope you can get thru the inspection without getting violations. Be there when the inspector comes and keep it friendly. I speak from experience. Once you are approved and have the license you are home free. Good luck.
I'm surprised when you purchased it that the previous owner did not convey that to you.
Yes the city Lake Worth can make your life miserable and will nickel and dime you any chance they get. Surprisingly Greenacres which is right next to it is completely the opposite.
I just bought a duplex in Lake Worth from a homeowner who was going through the exact same thing. Lake Worth is a beast, but once you get in compliance you'll be fine. Talk to a few of the field guys also. They'll take care of you ;)
Agreed, the initial inspection they can write you up for multiple things, after that you are ok. Let us know how you make out.