Take a look at this Python library:
python-litecoin-utils.
https://github.com/karask/python-litecoin-utils/blob/9e395f1281e3c84c5ff4644acb47be99e6205022/litecoinutils/keys.py#L177-L185 """Returns key in WIFC or WIF string
| Pseudocode:
| network_prefix = (1 byte version number)
| data = network_prefix + (32 bytes number/key) [ + 0x01 if compressed ]
| data_hash = SHA-256( SHA-256( data ) )
| checksum = (first 4 bytes of data_hash)
| wif = Base58CheckEncode( data + checksum )
"""
Litecoin does seems also uses SHA256 and Base58Check. The only difference is in the version byte code. You can also refer to that about how to extract the public key and the address, just take a peek at the code since it is also available.
If you'd like to do that on JavaScript, I'm sure there is also a library for it, just search around about it.
