It's not really my thing, but it's best uses are for trading, imo. One can move a million dollars from one exchange to another exchange, operated out of a different continent very quickly and without the amount or even asset type being viewable. (Liquid confidential txs hide both amount and asset type, so you dont "announce" trades) This makes it perfect for arbitrage.

Normally, an arbitrage trader would have to have some funds on all exchanges, because they wouldn't be able to fund a particular exchange fast enough. Especially in this environment, reducing your need to keep funds "hot" (on exchanges) is pretty cool.

Again, another usecase that is not my cup of tea, is they have tokens that can be whitelisted for certain addresses which are registered to "qualified investors." These tokens are actual registered securities or equities (like stock shares.) Pretty sure this is what El Salvador is doing for their "Bitcoin Volcano Bonds."

Samson Mow (ex Blockstream, current Jan 3 CEO(Jan3 is a company promoting and aiding Nation-state adoption) is working on a videogame with a liquid token as the in-game currency, and the keys to spaceships being Liquid NFTs. It looks... actually top tier good, not just good for a blockchain game. https://www.infinitefleet.com/

Tdex is a Liquid Dex, if thats your kind of thing. (Heres an instructional video from the wonderful BTCsessions: https://youtu.be/5DBqP3MtG34)

As far as wallets go, green wallet is the software wallet and jade is the hardware wallet that allow btc, L-BTC and L-BTC assets.

Also Aqua wallet, (which hasnt been really worked on for a few years(and was only avail on iOS,) aiming to be very user friendly version of green wallet,) is now being revived and worked on by Jan3, so a new version should be released in the near future, promising easy BTC to L-BTC USDt transfers in-app, as well as Lightning. Which is cool, as far as i know, there are no mobile wallets that have LN and L-BTC.