Never flown Turkish but here is some general advice based on booking other partners.

So long as your payment to Lifemiles has been processed and you have a Lifemiles confirmation and ticket numbers you have verified by checking it on avianca.com ("Manage your booking" tab), including verifying you have ticket numbers issued, you should be OK so check that if you haven't already. If a schedule change shows there you should confirm it which can usually be done there (Manage your booking on avianca.com).

It is also good to check the booking on the Turkish website. If the Avianca PNR doesn't work to retrieve it you need the Turkish PNR which you can either get by calling LifeMiles (avoid if possible due to long hold times) or some other method. IIRC, you used to be able to find the partner airline PNR by looking up your booking on the phone app but maybe it was just the ticket number. For some reason they did not used to show the partner PNR on avianca.com. I cannot remember whether I used the Avianca app or the LifeMiles app. Try them both. If you cannot retrieve the TK PNR there then other alternatives to calling LifeMiles are using checkmytrip.com which usually will show the partner PNR, or you may be able to up the LifeMiles PNR on another Star Alliance airline site which may give the partner PNR (maybe try united.com?).