Here are all the lockpicking angles I use in my Any% V2 Speedrun:

US Embassy

UpL, LowR

Cryogenics Lab

-> 1st: LowR, UpR, LowR

-> 2nd: LowR, UpL, UpR

-> 3rd: UpR, LowL, UpL

TV & Radio Broadcasting Station

-> 1st: UpL

-> 2nd: UpL, UpR

-> 3rd: UpL, LowR, UpR