I believe you have a few things to try however it may take some time and some help to get you through it.
I believe it may be possible to get your bitcoin private key and gain access to that account on the litecoin blockchain.
Its a process that has been used quite a few times when people make chains that bitcoin owners can claim the same ammount of (whatever coin) that they had in bitcoins on the new blockchain. lumens did it i believe and some others.
I would suggest going and doing this first.
And then start by trying just trying to gain the private key of the bitcoin electrum wallet and restoring it on the litecoin electrum wallet. It may not be that simple but its worth it as a first step.
My second suggestion is to do what these guys are suggesting here. Post #16
They are walking through a process that may seem daunting but really is made easy if you're using the electrum wallet.
You are surely going to need some help with all this if you get stuck. I think the biggest tip i just gave is that its been done before for new blockchains allowing bitcoin holders to claim stake. it is a idea of fair distribution or whatever.
Let us know how you go. I personally have not had to do this but i understand that you can infact send litecoins to a bitcoin address of this type. Being that Litecoin uses the same '3' prefix as Bitcoin for P2SH. Good luck and hope this helps a bit.
Please not that electrum also support a litecoin wallet.