I scored a 112 on the DLAB and would like to learn Russian, if possible. Can I request or influence what language I’m assigned at DLI?

You can request anything you’d like. However, your language will be assigned based on needs of the Army. With a 112, expect a cat4 language. I see MSA, Chinese or Korean in your future.

I went through SOLT but it is overseen by DLI, I scored a 127 on DLAB. They wanted me to learn Thai, but I worked my way into Russian. So 127, assigned low cat 3 and got into high cat 3 language.

Kinda of, It's not likely that you will get Russian but there is a chance for that but Russian is one of the hardest languages to learn at DLI and they usually want people with a higher DLAB score.