Buy LTC on localcoinswap (does not need KYC and is P2P), through sites that accept card but don't KYC (you can find some on the Cake Wallet app) or via a normal KYC crypto exchange and them swap it to XMR using a privacy focused CEX/CEX Aggregator or DEX. Two good CEX Aggregators are Trocador and OrangeFren, they will probably give you the best rates too, but depending on what CEX they choose or the source of your LTC it may require you to KYC. A good example of a privacy focused CEX would be Infinity Exchanger as they are JS free and run on TOR. If you want to go the DEX route BasicSwap would currently be your best option, however it does requrie some setup first.
Another option would be to buy XMR directly via P2P on RetoSwap with somthing like cash via mail. However to date I haven't been able to many AU based sellers.
If you've never used XMR before I would recommend reading some of the posts on /d/Monero so you know how to safely use XMR (the TL;DR would be to use local node or run your own remote node that you control, malicious remote nodes can be used to find your IP address and trace your transactions.)
Appreciate the replies. It's going to be a while for this old dog to work out cake wallet. I downloaded one yesterday and all I see is a bunch of files on my computer and f...n idea what to do next. My brain hurts with all this new stuff. Hopefully there's a tutorial out there. Monkey see monkey do.
Those devils at Abacus have much to answer for. I wasn't ready for a prolonged stint of sobriety.
Hopefully another market that accepts BTC comes along.
Forced to by the remaining markets mainly only accepting XMR. Same reason a lot of us finally made an account on dread instead of just clicking the links we need or just reading a topic. Sign of the times.