ok, how did you get the address? you had to generate it, or some site had to generate it for you.
you cannot generate an address without generating a private key as well. Also - fyi - the address IS THE WALLET you can open it with many wallet apps and programs but the address is the wallet, and if you do not have the private key, then you do not have the wallet or the funds.
So, either you mined it or you bought it. Either way, you had to generate an address and during that address generation they would have provided you a private key.
next, you have a wallet.dat file — that means at one point you had the Litecoin core wallet installed - is that a recent install and thus the wallet.dat file is empty? Or is that the old wallet.dat file from when you got the coins?
If that is an old wallet.dat file that is most likely where you coins are - just install the newest version of Litecoin core and open that file, I suggest you make a copy of it and store it in another location so that you don’t take a chance of overwriting it with the fresh install.
This may all confuse you and sound complicated but once you understand how it works, it is rather simple.
also if you could share the full address - the public address, that might help as well. I can see it partially as LQPnfjZzeo4hkb…