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It looks like a species of Euphorbia. There are thousands, and pinning this one down will be difficult.

The fact that it is having difficulty growing, even though it is highly invasive, tells me that you have a very bad infection in your lawn. Perhaps it remains too wet.

Unfortunately, killing your entire lawn and starting fresh is ideal. Fungicides will not, likely, help you here. Solarizing the soil will be a good start.

This article will help:

https://www.gardeningknowhow.com/garden-how-to/projects/how-to-solarize-garden-beds-to-eliminate-garden-pests-in-the-soil.htm

Be sure to follow all instruction that are on the package. I would not foliar feed AND root feed, together. That will be far too much on the plant. Only do so, as needed. Generally, this is done when correcting soil nutrients is too slow, or while soil is being amended back to a proper pH, in order to facilitate the uptake of nutrients that are unavailable during this time.

Be sure to test your soil before adding nutrients, so that you do not throw off the nutrient profile of the soil. This can do more harm than good.

Here are some articles that will help:

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/macro-and-micro-elements.htm

https://www.gardeningknowhow.com/houseplants/crown-of-thorns/growing-crown-of-thorns-outdoors.htm

It could be! It could be the sap latex, or other things, as well. Unfortunately, your photos did not come through, so I am unable to say what the issue is.

In the meantime this article will help you to care for the plant:

https://www.gardeningknowhow.com/ornamental/cacti-succulents/euphorbia/moroccan-mound-succulents.htm

Yes, the foliage should grow back, but it likely won't bloom again till next spring.

https://plants.ces.ncsu.edu/plants/euphorbia-amygdaloides-subsp-robbiae/

Unfortunately, diseases happen! Sometimes, no matter how proper the care routine, it can still get infected by something.

I would try and separate as many of the healthy growth and portions of stem that you can, in hopes of getting a clean sample. Using cinnamon, and other fungicides before planting can help, drastically, as well! This article is for a different type than yours, but you can use this information for all of the Euphorbias:

https://www.gardeningknowhow.com/ornamental/cacti-succulents/euphorbia/euphorbia-stem-rot-issues.htm

This collection of article will offer more information:

https://www.gardeningknowhow.com/ornamental/cacti-succulents/euphorbia

Likely, it has run out of room for the roots. A larger container with fresh cactus soil will likely get it started back up.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/scgen/cactus-repotting-info.htm