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This article will help you.

https://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm

It could be a watering problem. This article might help you:
https://ask.extension.org/questions/286404

Sunburn and cold weather could also cause brown needles. Check whether anything could have changed in the tree's conditions or environment.

I'm in the school of thought that this is a unique idea, but there are too many unknowns for me to make an exact recommendation.

Different trees and the type of bark that the tree has, could react differently to this process.
Trees need to breath and even using a natural clay product could compromise the trees.

You could contact the manufacturers of the products you are using to determine the safety of the paint for use on a living tree.

With this being said, painting tree trunks with water based paints is a process that is used at times to help prevent sun scald.
Here is an article about this process.

https://www.gardeningknowhow.com/ornamental/trees/tgen/painting-tree-trunks-white.htm

I do not know the variety of tree that you are referring too.

Here are some articles that may help you.

https://www.gardeningknowhow.com/ornamental/trees/tgen/trees-with-invasive-roots.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/problem-tree-roots.htm

It will take forever to kill a tree this way and in the meantime, you'll ruin the soil. The easiest way to kill a tree is to "girdle" it: remove 6" of bark and the inner cambium layer all the way around the trunk.

First year tree and shrubs need water right up until snowfall if there isn't rain. When a tree, shrub or perennial goes into winter dehydrated, its chances of surviving the winter decrease and the risk of winter die-back increases.