I'm probably doing this wrong but thought it would be fun to try...
I wrote a bit of python to iterate over adding in a character from 123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz at every space and check if a valid bitcoin address was found.
a few oddities stood out imediately though...
The private key given is 52 characters long just like an uncompressed key would be.
The compressed key should be 53 characters hence why I think you're asking for the missing character.
What is weird is the private key has a lowercase L (i.e. 'l') in there... this therefore can't be a valid base58 value.
I tried replacing the L with a 1 and this generates an invalid private key so instead treated it like a brain wallet doing a SHA256() on it giving the address 1LgcRxRoTcx7pZWXdBNWHBUaoZpsEsU8uK which has 0 funds in it so looks a dead end.
I also tried brain wallets by just removing the 'l' character and again no funds at the address 13KK9xSXXrN6MS4P1hAMrB5V5q8ehLAmJg.
I also tried running through all the characters replacing that 'l' but no valid private key could be found.
Without knowing a bit more information about this it's really hard to know what is happening with this.
Are you certain it's a private key?