Yes, you will - probably!
The LOT website contains the details for eligibility to access the lounge, which includes :
- e) Passengers in Business Class in transfer to domestic flights – if
passenger has a boarding pass for a domestic flight in economy class
and the previous or next leg of the journey (to/from WAW) is in
business class with Star Alliance carrier, passenger has an access to
the Lounge. In this case, the journey must be made on one ticket
issued for the entire route in business class.
The wording here is a little confusing as it talks about the entire route being in business class, but the flight being in economy. Most likely this is referring to the details of the way the route is priced, and matches what you've described where you basically have a business class ticket, but are seated in economy due to the lack of a business class cabin on that flight.
Realistically the fact you arrive on a business class flight is almost certainly going to be enough to get you in, without even worrying about the way the ticket was priced/purchased.
Note that in general across Star Alliance carriers the above conditions are NOT always the case. Star Alliance lounge access rules are based on the departing flight only, and as your departing flight is not in business class you would not be eligible. However individual airlines are able to extend these rules - and many do for this particular case (arrive in international business, depart in domestic economy), as LOT has done.
Having said all that, don't set your expectations too high for this lounge. Whilst there's nothing wrong with it, and it's far better than spending your time in the general area of the airport, it's certainly not going to come up to the standards of the lounges you'll have access to in London Terminal 2 where you'll have access to any/all of the United Airlines, Singapore Airlines, Lufthansa and Air Canada lounges!