litecoin constants and prefixes
Here is what I've gathered so far regarding the different version bytes for each type of Litecoin public address:
Mainnet:

p2pkh L-address (LM2WMpR1Rp6j3Sa59cMXMs1SPzj9eXpGc1): 0x30
p2sh deprecated 3-address (3MSvaVbVFFLML86rt5eqgA9SvW23upaXdY): 0x05 (same as bitcoin's mainnet p2sh)
p2sh new M-address (MTf4tP1TCNBn8dNkyxeBVoPrFCcVzxJvvh): 0x32

Testnet:

p2pkh m- or n-address (mipcBbFg9gMiCh81Kj8tqqdgoZub1ZJRfn): 0x6f (same as bitcoin's testnet p2pkh)
p2sh deprecated 2-address (2N2PJEucf6QY2kNFuJ4chQEBoyZWszRQE16): 0xc4
p2sh new Q-address (QVk4MvUu7Wb7tZ1wvAeiUvdF7wxhvpyLLK): 0x3a

This is the Litecoin project's converter between old and new p2sh address format.
And this is an online base58check decoder to check the version byte.