If LOT made you miss a connecting flight because your first flight was delayed, you’re often entitled to compensation under EU Regulation 261/2004 since LOT is an EU carrier and the whole itinerary was on one ticket.
Under EU261, if the delay caused your arrival at the final destination to be 3 + hours late and the disruption was LOT’s responsibility (not extraordinary circumstances like severe weather), you can claim up to about €600 per passenger depending on the distance and delay.
You should first file a written claim with LOT Polish Airlines customer relations citing EU261, your booking reference, flight numbers, and why you believe the delay was their responsibility, and ask explicitly for compensation plus reimbursement of any out-of-pocket costs (meals, hotels).
If the airline refuses or ignores you, file your complaint on Xolvie to pursue a resolution.
Related Complaints
LOT Polish Airlines Delays and Poor Service Ruined Istanbul–Krakow Trip

Our round-trip journey with LOT Polish Airlines from Istanbul to Krakow and back turned into a complete ordeal. Our outbound flight was postponed by three hours and then rescheduled for the following day. During this entire waiting period, passengers were not attended to at all, and no refreshments ...