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This could be a type of scale, or mealybug. It would help to have a picture for identification. There are a few things that you can do to help smother them, though. Neem oil is a good way to do so, as long as you do not apply in direct sun.

This set of articles will give you more ways to control insect issues: https://www.gardeningknowhow.com/special/organic/

In container, these can be difficult to keep unless you have a few things handy. You will want to always have, on hand, dolomitic lime, and iron sulfate. Mix these in twice a year, and feed a good granular fertilizer once per year.

The most likely culprits would be, lack of potassium, and phosphorus, OR a severe pH swing... This would be the more likely reason.

Both dolomitic lime, and iron sulfate will keep the pH where it should be, and provide magnesium and calcium. These two will always be lacking in container citrus.

This article will give you more information: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-lemon-trees-containers.htm

It is not sooty mold, but it is a severe insect infestation. It looks more like a type of aphid causing this, though. There are many natural remedies that you can use to clear this up. One of my favorites is neem oil.

Here is a collection of articles that will help you get rid of this problem: https://www.gardeningknowhow.com/special/organic/

Freezing temperatures will, definitely, hurt the fruit. If you can bring it indoors during this time then you will not have to pluck the fruit. If this is not possible, then the fruit will drop naturally if they are harmed to the point of death. Here is an article that will help: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-meyer-lemons.htm

I forgot to mention, he left a few pieces of fruit on the tree from last year, so i dont know if this was one of those but it was soft when squeezed but not mushy?

So far, the fruit drop you've described sounds normal. Meyer lemons are small trees, and they can't support all the lemons they first produce, so they naturally drop most of the fruit (especially when they're relatively young).
https://www.gardeningknowhow.com/edible/fruits/lemons/lemon-tree-fruit-drop.htm

If your tree drops its remaining fruit, this can be a sign of poor health or stress. Check the tree carefully for any pests or disease issues, and make sure the watering, fertilizer, and light levels are correct for that tree:
https://www.gardeningknowhow.com/edible/fruits/lemons/growing-meyer-lemons.htm
http://extension.oregonstate.edu/gardening/meyer-lemons-can-be-grown-pnw-if-protected-winter