Should I give a healing item to my follower?

It's possible that it could be of some small use, but there are a few relevant things to remember about followers and lifesteal items:

• They gain a 2.5x multiplier to any stat items on them (including Vitality),
• unless a concerted effort is made to boost them, deal significantly less damage than a player would,
• most lifesteal items operate on a percent of the damage done,
• Followers suffer no penalties for dying save for a brief delay before getting back up.

Even with strong weapons on the Scoundrel, from what I've seen it's not a great benefit, due to the low damage potential of even the most kitted out followers.

The best things to stick on followers for general use are still weapons with decent DPS that you don't think you could sell for much, as a small amount of damage is still extra damage; and items with large amounts of statistics - the Scoundrel can turn a +50 Dexterity weapon into a +125 Dexterity weapon, the Templar can turn a +50 Vitality shield into a +125 Vitality shield, so on and so forth.

Well, the first question is, how often is your Templar actually dying on you?

I don't know about you, but for me, the Templar only really dies when the shit is hitting the fan, or if he gets burst down by standing between me and some Fallen Maniacs or other similar one-shot gimmicks. In either of those cases, a little bit of extra life on hit just isn't going to save him.

I find that your best bet in gearing your companions is to prioritize, more or less in order: Weapon DPS, Primary Stat, Vitality, and Magic Find/Gold Find/+XP. If your follower has 'enough' defense to not be dying regularly, stacking MF/GF/XP is probably the most useful thing you can do, simply because it's the only one that directly benefits you. They get the vast majority of their damage output from having an up-to-date weapon, and even then, their DPS is generally pretty pathetic - the main advantage of a follower is the CC, Healing, or Buffs they provide for the player. In my experience, your best bet is to play to that strength, and gear accordingly.