Mguess, no you do not need another tree for your citrus to bud/fruit. Do you place trees outside in summer? If possible, do so. The only duplicate trees I have are Kaffirs, and that was by accident. Still citrus fruit. So there's no need to worry..
As long as they're taken care of properly you'll continue getting fruit..Toni

No prob. all of your trees -are- self fertlizing outdoors. If blooming happens indoors I enjoy helping them out.
When the flower has been open for about a day they will have a darker pollen then they are ready to pollinate just brush ever so lightly the pollen on to the sticky tip of the center of the flower. Once pollinated the flowers pollen will become a lighter in color. Just be gentle and you only realy have to do it once. I just use a small piece of clean paper towel twisted into a thin 3-4" long stick for a pollinator. You can also get at almost any store a childs small paint set and use the clean never used little brush to pollinate. They are around $0.99 and are worth it if your tree is large. After that in a couple of days and all the petals fall off you'll see the beginnings of a citrus fruit. When they are young or stressed alot of the flowers/young fruit will drop. Do not worry it will slowly but surley year after year hold more and more fruit, till your giving bags of them away!
Cross pollination between the different ones would not matter to you unless you want to raise hybrids from the seeds.