After many tries I have come up with the following Lyonar List
Any suggestions to improve it to help me to ladder.
Help me to improve this heal Deck
i posted a healonar deck not too long ago
Check out this post, tons of information. I skimmed through it just for the read. I plan on making a healyonar deck after the next expansion after they hopefully release more heal synergy cards.
I can’t really give advice since I don’t play Zirian at all, but have you tried experimenting with Circle of Life? It does cost a lot, but 5 damage/heal is pretty strong. You can take out just about anything with a general attack combined with the damage and heal yourself back up. Works great against Spectral Revenant, Aymara Healer, etc…
I’m not sure how much help I’d be beyond Rank 5 as that’s the highest I’ve gotten to and I’m already having trouble keeping up, but I think you should focus more on healing synergies to buff up your minions and Zir’an.
With that said, perhaps remove Slo, Azurite Lion, one or both Emerald Shrouds, and Inquisitor Kron. The latter two were nerfed recently, and whilst still playable, there are better options. Try adding some Lightchasers, one or two Circle of Life, and maybe even a couple of Divine Bond. I’ve used Divine Bond right until I reached Diamond, and it has worked great.
Some say if you’re using that card, you might as well use Argeon, but I dunno… healing synergies are great, but it doesn’t always work out, so it’s nice to have something to fall back to, and since you have Ironcliffe and Z’ir, Divine Bond might prove useful in certain situations.
Finally, you have 8 healing triggers (Fiz, Healing Mystic and Day Watcher), not including Afterglow, however only 4 minions that benefit from that trigger (Sunforge Lancer and Sunriser). Most of the healing triggers are low mana cards, and you might even be wasting one or two before you even get a Sunforge Lancer or Sunriser out. Hence, the suggestion for Lightchasers.
Everything else in your deck looks pretty good to me! 
Try to fit some Sundrop Elixers. It is the easiest way to proc heal effects.
I would also say put a 3rd beam. Beams are lovely
Also maybe a bit more card draw somewhere. Heal combos burns cards quickly.