Bethany is a town in Israel, mentioned a number of times in the Bible.  It was a place that the Lord Jesus loved to visit, and was the home of Mary, her sister Martha and Lazarus. Bethany itself means "house of figs", and its a nice coincidence that Bethany just happened to be born in Figtree private hospital!

Possibly the most notable thing about Bethany mentioned in the Bible was that Lazarus was resurrected from the dead by the Lord Jesus there, after being dead some four days.  It is something that we were reading around the same time and took on new meaning after Bethany was diagnosed.

The following thoughts are from a little booklet "Bethany" by and Christian brother named Bakht Singh (Chapter 2 - Resurrection Power).

In John 11:1-3 the sisters sent for him to come home, because there was a special need at that time.  Their brother [Lazarus] was very sick.  They did not know then what a great blessing the Lord Jesus Christ had in store for them by not coming immediately.

In the beginning of our Christian life, we go to the Lord only when we are sick or in any need.  We pray only for our personal needs or problems.  In John 11 we find the Lord purposely went late to Bethany.  Even though the sisters had sent for Him, He did not go immediately (v.4) because He had in His mind to give a greater blessing than they had asked for.

They wanted Him to come and heal their brother who was very sick.  This is how we too pray in the beginning.  We think only of our personal need.  At that time the need of the family was very great and urgent.  We find however, that when the Lord delays in answering prayer, it means that He wants to give us a greater blessing.

The Lord purposely delays going so that He might show the family and the people His true glory and give them a personal experience of the power of resurrection. 

The Lord Jesus Christ went to Bethany so that Martha, Mary and Lazarus might know Him more intimately, and so that they might have a personal experience of the power of resurrection [from the dead, something far greater than just healing his sickness]. 
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God permits in our lives many painful situations and circumstances that we may have an opportunity to prove his faithfulness, and so that the power of resurrection will come more and more into us.  Such an intimate knowledge of God comes by resurrection power.

We were very encouraged here that the Lord's purpose was to bring an even greater experience of the Lord's power and love, and to achieve that purpose he actually waited until Lazarus was dead.  The Lord could well have healed him of the sickness before he died, but he wanted to bring not just healing - but also faith and belief - a deeper knowing of Him - not just that he can heal sickness, but he can bring life to the dead even.

In John 11:40 Jesus says to Martha, "Said I not unto thee, that, if thou wouldest believe thou shouldest see the glory of God?".  We know that with Beth, the Lord can well bring healing, if he so desires, and we pray for that, according to His will; but we are also comforted knowing from here that His answer may be delayed; but it will be for a wonderful purpose - that we, and you might believe in Him see the Glory of God more in our lives in a deeper and richer way.