There's a Plaza Premium Lounge in LCCT at KUL (and also another in the main terminal). I've not been to the LCCT one, but I think it's very similar to the one in the main terminal, which I have been in a few times. You can get a shower (they'll provide towels and shower gel), which I find nice between long flights. They have a large number of chairs, some with power points, some comfy sofa like ones, some at tables etc. There are a small number of newspapers (not a great selection though), some magazines, and a TV or two. There should also be a few massage chairs, but they're very popular. There is WiFi available, and a few computers to use. Food and drink wise, there ought to be a handful of different simple hot meals available, mostly Malaysian style, along with some snacks and fruit. There's beer, soft drinks, coffee etc. It's certainly not a high-end lounge like you get with a lot of the big flag carriers, but it's certainly above average for third party lounges.
Access to Plaza Premium lounges is covered by a range of programs, so it may be worth checking if you already have access. I know that Priority Pass gives access (that's how I get in), as do a range of higher-end credit cards. I don't believe that the Plaza website tells you about which cards have access, instead you'll need to check with your credit card about if it's in their lounge program or not.
Alternately, you can pay to get in. You can just pay on the door, but you can normally get some much better deals if you book online in advance, through a third party website. The headline price at the lounge is Rm118 for 2 hours, Rm158 for 5 hours. If you hunt around online, you can probably get it for about a third of that (I'm pretty sure I found a hefty discount the one time I went before getting a Priority Pass. A quick google found 3 hours for £20, or 6 hours for £27.50, on a respected lounge access website, you might well be able to beat that).
(There's also a higher risk option, which is to hope you manage to make friends with someone with a Priority Pass or similar, who's able to guest you into the lounge. If you don't find someone, then you'll be stuck having to pay the full fee on arrival to get in. You might have some luck if you find someone on a suitable FF forum, and arrange something in advance)