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:
Thanks! This is what I expected, but wanted to confirm. Now to decide if a 1hr 40min offline connection in IST is worth it...