Don't know about the white spots but the brown lumps look like scale insects. Here we would spray with white oil to smother the little so and sos, but not on a very hot day. This may also clear up the white dots, if that is a similar critter.

Looks like scale, all of it. Neem oil applied repeatedly will smother the scale. This little tree is very heavily invested, so this will take multiple applications. You don't mention if the tree is indoors or outdoors or where you live, so Coleen's advice is good - do not apply any hort oil if temps are above 85 degrees F.

Patty S.

He said in a south facing window which should imply indoors.

Dichlorvos. I can't say enough about this stuff. Besides don't breath it.
The product you want is hot shot no pest strips. Stick it in a closet at night with one for a week. No sprays, no bugs. No chance of burning the plant.

I find this publication very useful:

Here is a link that might be useful: Integrated Pest Management for Citrus

Here's all you need to know about managing citrus pests -- see the link

Here is a link that might be useful: citrus woes

Thanks for the advice! I'll get to work with treating the poor tree. I am in Chicago area, so no risk of too much sun and high temps in my living room!

Pip....you have GOT to be kidding about your recommendations for dichlorvos! I hope that anyone tempted to hang No Pest Strips in their closet for a week will spend two minutes doing the research about this very dangerous product.

Don't do it.

Do it all the time. Like I said don't breath it.

If your chest hurts a little breathing, your breathing it too much. The whole idea is to seal it and the plant in their own room. I always put a towel in front of the door, shoulda mentioned that. Sorry