it looks like it was set in Minion Black - and the tops were modified

a little note to add

The script looks like it was created by the person who made these fonts
https://www.dafont.com/nug-s-project.d7594?text=Beach+Erotic

Also the"E" seem to match up with the E in The Lunatique

Limited may not necessarily be a font. The two I formations are different - however if you'd like something as a substitute SignDNA for "imited" had a font named Santa Fe. The don't sell it anymore - but you can see two examples here: https://signdna.com/search?q=santa

And for the "L" - take something like Angelface and fatten it up.

FF District Bold Italic

Not the font - just a substitute.

If it was polished it would have been a C from Plaza
Closest I can find with it's imperfections would be Class A

This is based on Bookman with Swash - closest I can find in today's font market is this

closest I can find

NOT THE FONT
But...maybe you can modify to get the results you seek.

SIMILAR

it looks like Clarendon made by a manufacturer who changed a few things... and then heavied up the bold.

settle for close?

NOT THE FONT

It looks like a modified version of Quantify

Similar - possibly stroked to make thicker?

This was probably hand-tailored to make a logo. You could come close modifying Zeppelin 41

NOT THE FONT