Str is the way to go as a healer, healing doesn't cost a lot of mana, so you are better off with more Hp so you can take a hit rather than dying.
However, the use of a Healer is a bit arguable. In general, you use it to heal up yourself or a teammate.
When you heal yourself, it´s only vs mobs, since if you go healing yourself in PvP you are wasting precious time dealing damage. The only time i heal myself vs mobs is when i run low on hp pots, so it´s only usefull to save on pots.
When you heal a teammate, it´s when he´s PvPing, on job or fighting uniques.
In PvP i don´t have a lot of xp with it, so i won´t discuss that now

Healing when teammates are fighting uniques is a nice addition, but i don't have much xp in fighting uniques, so can't really say anything about it.
On job, you only heal a teammate when he is fighting someone who is equal or stronger than him. Most likely the enemy is stronger as you as well, else you wouldn't need to heal your teammate, but just kill the enemy yourself. If the enemy has any braincells, he will go after you first, since you are weaker, and can't heal your teammate anymore. So the only thing you are good for is being cannon-fodder (which can be good, since your teammate can get some time buffing up or casting nukes), or be a real help if the enemy is a bit stupid.
This might be a big reason why a healer would go lightning (grasswalk), to be able to run from higher lvl enemies and running around trying to heal your teammates, while running away in time yourself when they come after you. I also wear garments, more move-speed and less mp costs, which both help. And if your grasswalk isn't above 50%, try to get some Move Speed scrolls.
Oh and with the monster summon scrolls/pandora boxes, it helped a lot too, healing up the int-people from a distance

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