As you can see I don't use any survival skills in this build (no healing or spell shields) but nevertheless I usually get killed a lot rarer than my fellow team members. It's because I stopped caring about the statistics of the match a while ago - Lunara doesn't have enough burst damage do get as many kills as Nova or other assassins. The best way to play Lunara for me is the hit and run method - since she's quicker than the rest of the heroes it's quite easy to get by. I don't chase running characters a lot unless I can be 99% sure there's no friend waiting for them that could kill me. You won't be topping takedown stats but you're going to deal a significant amount of damage and survive.

As far as I can see, most Lunara talent builds are similar - probably because some of the available talents aren't very useful (e.g. those that increase the range of Noxious Blossom). But my choices for Tier 1 and 5 may need some explanation.

1. I pick Cruel Spores because I think none of the remaining talents on Level 1 are useful. I'd hesitate sometimes and pick Natural Perspective but only when there are at least 2 heroes on the opposite team that use stealth a lot (Nova and Zeratul are deadly for Lunara when she's alone on the lane). Othewise - Cruel Spores are great for getting xp and later when combined with Invigorating Spores you'd be soloing mercenary camps or kill all the mercs that the opposite team just accuired.

2. Unfair Advantage/Giant Killer - I think both of them are worth picking. At first my choice would be Giant Killer but Unfair Advantage is very good as well. Both of the talents give you greater damage but Unfair Advantage is a little more situational: you slow down a hero and chase them while dealing more damage. Since I tend to avoid chasing (may be too risky) my first pick is Giant Killer. I still recommend both of those talents.
I can see that Greater Spell Shield is popular as well but since my way of playing Lunara is staying out of range and poking, I avoid taking damage in general and prefer damage increasing talents to shielding. I don't think it's a bad choice - just not my style is all.

Everytime I play I have to ponder a little on the choice here. It mainly depends on my comrades and the opposing team: how each of them play, on the map e.t.c. I find both of the avialable talents pretty cool. Thornwood Vine is easier to use when you want to stay away from the enemies but Leaping Strike is SO FUN I tend to favor it more. I admit that sometimes it's quite stupid.

When it comes to Level 20 talent the best choice in my opinion is the Galloping Gait talent. It's the ultimate escape way for Lunara since a lot of characters have stun spells or can raise walls that make me an easy prey. Galloping Gait has a quick refresh time, uses no mana and literally no one can run that fast.
The two talents increasing effects of your ulti seem all right but as I've already said, my way of playing Lunara is not really about a massive amount of takedowns (I deal a lot of damage anyway) - more about hitting, running and irritating the opponents (hey, it's fun). Abolish Magic looks interesting also but it also doesn't fit the 'hit and run' style of this build.