Fielding Luna means only one thing - shuffling 3 copies of Eclipse into your deck. Her stats are quite good for a blue hero, so it can help you cast Eclipse and other powerful blue spells.
Luna's stats are fairly decent. She has the second largest health pool in blue at 8 (tied with J'muy), and behind Kanna's 12. Her attack of 3 is a blue norm, sharing the value with multiple heroes and only losing out to Meepo's 4. Her 'durability' is well suited to assist casting your blue spells.
Luna's passive ability has 2 components: Random damage and the Eclipse growing effect. 1 random damage is cute and thematic, but it is neither reliable or powerful. The other half however...
Increasing Eclipse by 3 damage each time Lucent Beam procs is the real purpose here. Maximizing the amount of procs you get via survival and mobility (more on this later) is key to success with Luna. As such, simply having Luna in your decks acts like a magnet for removal - they WILL try to minimize your Lucent Beam procs!
Keep in mind that this happens before the action phase, so if you move Luna into another lane before combat, you get another proc. While this trick seems cute, one-sided Annihilations are not.
To summarize, it's effect is essentially a placeholder. The actual payoff is ramping up Eclipse.
We finally arrive to practically the ONLY reason to bring Luna into battle. Eclipse CAN BE the most powerful removal spell. The sheer fact you can wipe out your opponent's board and keep yours intact is unparalleled power. However, Eclipse comes with a hefty pricetag - effort.
Eclipse will always begin with one charge (three damage), even if you somehow never got a single Lucent Beam off.
More Lucent Beams equals stronger Eclipses, and there are a few ways to facilitate this. The fairest of which is SURVIVAL. Simply surviving means you get more procs. Simple enough. Any card that helps Luna survive indirectly helps you secure the lategame via Eclipse.
The second way is mobility. Switching lanes prior to combat allows you stack up Eclipse twice in one turn! While this isn't a sustainable method, it's something to keep in mind. Town Portal works too.
The final (and most important, but most vague) method is simply strategic outplay. Imagine stashing Luna away in a winning lane. What does your opponent do then? Commit to an uphill battle to stop Eclipse from growing? No matter how you play your Luna, keep in mind your opponent WILL try to disrupt the growth of Eclipse. Use this 'clock' to your advantage.
Given all this information its strikingly clear that playing with or against Luna is focused solely around managing Eclipse. The great thing about Luna is that her mere presence should warp you opponents gameplan. Use it to your advantage!
Sadly, like any hero whose power is heavily into their Signature Card - not drawing it essentially mean you're paying a huge tax for 'nothing'.
Blue decks want their blue heroes to survive so you can cast powerful blue spells. In Luna's case though, there is an EXTRA incentive to keep Luna alive. Your opponent also has EXTRA incentive to put her away..
Eclipse and Luna can act as a 'sidequest' for your deck just fine. You don't have to build around it completely. The mere fact you're trying to keep heroes alive is already part of the Luna gameplan anyway. 'Winning' is, after all, the best prerequisite for a safer Luna.
Ultimately, I think it's fair to say decks with Luna as part of their primary or secondary win condition would want to stall the game a little bit, making her more suited for midrange or control lists.