The united.com view of your reservation will give you the Lufthansa record locator, which you can use to view your reservation online at lufthansa.com (with last name & LH record locator). On lufthansa.com, you can assign seats for LH flights (and, in my recent experience, for TG flights on the same trip!).

If you'd like to know your Thai Airways record locator out of curiosity, you can e-mail [email protected] with your request. Unless something has changed recently, Thai does not have online seat selection for UA-ticketed award tickets — but you can also e-mail your seat request to [email protected] . Give them the dates of travel & name and you should be good to go; I also usually include the ticket number in case it helps. (You can get your e-ticket number by viewing "view receipt" on the united.com view of your reservation.)