LAX - DBV United, Lufthansa or ???

Looking at Star Alliance options for LAX - Dubrovnik in early October.
Want to fly “Premium Economy” (or whatever name specific airlines use).

Any recommendations on routes and airlines?

Looks like directly booking Lufthansa (or Austrian) Premium Economy is a better bet than booking economy and upgrading, right? And it seems booking through the Lufthansa website provides more options than United’s.