Q.Will lime trees like sandy soil?
Which lime tree variety is best for a sandy soil? We like the idea of a flowering fruit tree that is also fragrant. The soil where we are moving is a sandy soil. I have read that lime trees need good drainage. Will sunny sandy soil be advantageous in that regard?

Lime Trees can grow in a sandy loam soil.
The roots are fairly shallow and this soil type has good drainage.
You will want to add about 25% organic material to the planting hole. For a 12" planting hole add about 3 inches of compost to the soil area and work in before digging the hole.
Lime Trees prefer a soil Ph level from 6.0 to 7.5 with 6.5 being ideal.
You will want to have a soil test done prior to planting to make any adjustment to the soil.
https://www.gardeningknowhow.com/edible/fruits/lime/lime-tree-tips-care-of-lime-trees.htm