John 16:23-27:

And in that day ye shall ask me nothing.  Verily, verily, I say unto you, Whatsoever ye shall ask the Father in my name, he will give it you.
Hitherto have ye asked nothing in my name: ask, and ye shall receive, that your joy may be full.
These things have I spoken to you in proverbs: but the time cometh, when I shall no more speak unto you in proverbs, but I shall shew you plainly of the Father.
At that day ye shall ask in my name: and I say not unto you, that I will pray the Father for you:
For the Father himself loveth you, because ye have loved me, and have believed that I came out from God.

Notes on John 16:23-27:

Whatsoever” includes healing.  Healing is a subset of whatsoever.  Therefore, you can ask the Father for healing in the name of Jesus and receive it.  Jesus put no limits on this promise, and neither should you.

God wants your joy to be full.  If you are laid up in the hospital or your kid is dying of leukemia, your joy will not be full.  When you ask for and receive healing, then you’ll have great joy!  I’m not saying that you can’t still have the joy of the Lord when you’re sick – you can.  But your joy will be fuller if you’re healed!

The disciples could not pray in the name of Jesus during Jesus’ earth ministry.  Jesus indicated that the rules for prayer would change after His ascension.  Men would be able to pray to the Father in the name of Jesus, which no one until this time was able to do.  The “Lord’s Prayer” does not contain any petition to the Father in the name of Jesus, so there are plenty of things you can pray in the New Testament that are not included in the so-called “Lord’s prayer.”  So that prayer is definitely not an all-inclusive prayer for the believer.

The Father Himself loves you enough to heal you!

See also:

No Limits
Who You Are and What You Have
We Hold the Keys
Healing Is a Good Thing
How NOT to Pray for Your Healing
The Power in the Name of Jesus