BUT: you can probably use the swiss advanced checkin to select seats on the LX flight:

https://checkin.swiss.com/ck.fly

Use the LX flight number, and enter all the details for the LX flight (i.e. not the first flight, but specifically the LX flight)

I tested this approx 20 hours before an AC codeshare operated by LX, which was the third leg in a 3-leg trip (first flight operated by UA, second by AC, third by LX) - I'd already checked in with UA for the entire journey a few hours earlier.