While LO has interline agreement with both TK and HY, through check-in on separate tickets is NOT your right (even if interline agreement exists). Post-COVID there are many new agents, who might even not know how to add a separate connecting flight to your check-in record. Pre-COVID through check-in was never a problem with LO, though. Good luck...
GDS interline check display:
W/*LO‡*HY«
LO-080 LOT POLISH AIRLINES/POLSKIE LINIE LOTNICZE LOT
MAY ISSUE TICKETS INCLUDING
HY-250 UZBEKISTAN AIRWAY/UZBEKISTAN HAVO JULLARY
MAY CHECK BAGGAGE TO
HY
W/*LO‡*TK«
LO-080 LOT POLISH AIRLINES/POLSKIE LINIE LOTNICZE LOT
MAY ISSUE TICKETS INCLUDING
TK-235 TURKISH AIRLINES/TURKISH AIRLINES INC
MAY CHECK BAGGAGE TO
TK