You can select seats on LH if you book it with a LH flight number. If you book it as a UA codeshare then that's where you have problems.

As far as booking it via LH's website vs. UA's, you may actually end up earning more miles if you book it via LH, depending on the ticket price and your status with Mileage Plus. If you book via United then if you're a base member (your profile doesn't indicate any Premier status) then you only earn 5x miles on your fare (taxes excluded). If you book via LH then you get a multiplier of the actual miles flown which is somewhere between 25% to 200% depending on the fare class (first letter of the actual fare code). I don't know where you live but let's just make an example from EWR, EWR-FRA is ~7750 miles round trip. If you fly LH (and ticket with LH) then you'd get ~1930 miles on a K fare, ~3875 miles on a S, T, or L fare, ~5,800 on Q, V, W, and 100% of the 7750 on higher economy fares. Premium economy will get you 100%-150%, depending on the fare bucket. Now if you fly United, let's say your fare is $500 before taxes, it's a little trickier than this but for simplicity let's call that 2,500 miles (500x5). You'd be better off buying your ticket from LH unless you're buying a K fare. If you're looking at Premium Economy then you need to do the math based on whatever the fare price is.