Well, I planted this Lime tree one year ago, and know it has gotten these strange whitish fungus-like growths as shown on attached photo. I live in Thailand - that is tropical climate.
Nyles, Your tree does not have a fungus. It has mealybugs. Sorry for the bad news. They are a nasty pest. Mealybugs suck sap from plants and can pass diseases. They are easiest to control when they are newly hatched (called crawlers). The crawlers look like tiny bits of gook and move around. The adults stay in one place and grow the fuzzy mealy looking coating. That coating is what makes them hard to control. Sprays will roll off without ever penetrating the fuzz. You can control them several ways. First I take cotton swabs or something similar and wipe off everything possible. Then take clean swabs and dip them in alcohol and rub the area down. That gets what is visible. Next spray with an insecticidal soap. Be sure you spray into every crease and crevice. The crawlers can hide in the tiniest spaces. The soap will dry out any insects it is sprayed on. Check every week or so. Getting them all in one attempt is almost impossible. You may have to go to a light horticultural oil. That will coat them and smother them. Once you have fruit on the tree don't use any chemical that you put on the soil. Systemics get into the tissues and stay there for some time. Controlling mealybugs is time consuming and frustrating but can be done. I've personally cured some pretty bad infestations on some houseplants but have had to destroy others. Just be faithful and you should do fine.
Thanks a lot sabagal. I will try out Diazinon. I looked up those bugs, and Diazinon seems to be effective - if I can only get it here in Thailand :-) Thanks again!