Hello! I would be grateful for any advice on this. I need to fly Athens, Greece ATH - Houston, TX IAH on June 2. I'm hoping to be upgraded with my Plus Points on a LH flight (connection in Frankfurt.) The United website doesn't let me buy Economy and be waitlisted for this flight, but the United website seat map shows 20 seats to select in business class. That makes me optimistic?
I can buy this flight in Economy or Prem Economy (Prem would give me a better chance of being upgraded?) on the LH website. Can anyone please let me know if there are I fare classes available - meaning, would my Plus Points clear? I know I have to apply for this directly on the United website PlusPoints Upgrade Request Form and wait to hear. Here are the flights - of course I'm more concerned about being upgraded on the 2nd leg (not the first one!) Thank you so much for any help or advice!

Athens - Houston

Departs on Sunday, 2 June 2024

Total duration: 18h 40m

Total duration: 18 hours and 40 minutes
3h 5m
07:05Athens
Athens International E. Venizelos (ATH)
09:10Frankfurt
Frankfurt International (FRA)
Terminal 1
Flight duration 3 hours and 5 minutes
LH 1285 operated by Lufthansa

AIRBUS A3211 stop in Frankfurt International
4h 45m
Duration 4 hours and 45 minutes10h 50m

13:55Frankfurt
Frankfurt International (FRA)
Terminal 1
17:45Houston
George Bush Intercont (IAH)
Terminal E
Flight duration 10 hours and 50 minutes
LH 7601 operated by United Airlines
BOEING 777-200/300