Prayer loneliness might mean different things. It might be a prayer for loneliness, literally. You need to pull away from people who are unhealthy so you can seek change. It might be a prayer for loneliness in the sense that you want prayer to be the means to find the answer to the pain of loneliness.
An example of a prayer to be delivered from loneliness can be read in Henry Van Dyke’s book The Spirit of Christmas, which provides the experiences of having dealt with reoccurring holiday loneliness.
The Bible book of Psalms offers up a prayer for loneliness: Turn to me and be gracious to me, for I am lonely and afflicted. Psalms 25:16
Check out this wonderful Prayer for Lonely People on beliefnet.com. It was written by Vienna Cobb Anderson.
If you are lonely and looking for companionship, this prayer may be helpful to you: Pray of Loneliness For Companionship by Earnestine.
A Christian counseling site offers a lot of helpful information to you if you are suffering from loneliness in addition to a prayer and the means to request that others pray for you.
Finally, this site offers a whole set of prayers for the lonely for your strength and comfort. It even includes a prayer to bless an empty house.
Let these prayers inspire you, and create your own, personalized to your emotions and needs. The comfort of uttering a prayer comes in the way that you are also professing hope.