Hello,
Whiteflies are very fond of citrus, so it is no surprise that you have noticed them on your lime tree. The detergent mixture should help to reduce the infestation, but if the population is high it would be wise to use a stronger insecticide before the pests spread to your other plants. A great product to get the job done would be SNS 203. It is a concentrate but the directions to dilute it into a spray bottle are very simple. Additionally, this product can also be mixed and poured into the soil, thereby killing pests in the soil while simultaneously killing pests on the foliage when sprayed. This way you can be sure to eliminate pests in both environments. Please see our article on whiteflies and links to the mentioned products below.
Good luck!