Why is my Spanish Lavender dying?

Are there drainage holes in that pot? https://www.gardeningknowhow.com/edible/herbs/lavender/growing-lavender-in-pots.htm

depending on the drainage of the pot, the consistency of the soil, once a week may be too much .... especially if you get much rain.

Try adding some sand and/or fine gravel to the pot. You may find that in order to save the plant, it might be best to plant it directly in your garden. I see you live in N.C. ... perhaps, it’s too hot in the Summer (and it might prefer a semi sun exposure) although that said, my son has huge lavender beds that receive full sun. Yes, we both live in Canada but in southern Ontario, Summers can bring us weeks of 90F plus temperatures. Two years ago, we had very high temperatures for well over four months. The tobacco farmers up here sure were happy! lol!

PS: I also forgot to add that the soil might be depleted (too old). You could try giving it new, slightly sandy, soil. Good luck!

It probably can be saved. If you cut into a center stem, about 4" from the root, and the stem is green - not dead, then it does have the ability to come back. Most Lavender has a bit of a woody stem. It IS pretty hardy, and IS drought tolerant. But, unless/until it is established, it needs care like every other plant. You do not say how long it has taken to deteriorate. Everyone had great suggestions. so I will recommend the following to start over. Repot using fresh potting soil, not planting soil which is for the open garden. Potting soil has more nutrients, and retains a little more moisture. The water needs to drain away from the roots. If the pot doesn't have drainage holes, and you can't drill, or cut them, you need to create a vacant space in the bottom - maybe about 3". A layer of large rocks (or large chunks of cut up foam from Dollar Store pool noodles). Replant, insuring the soil surface is about 1-2" below the pot edge. Water to root level.

Now, back to the stems, take sharp clippers and cut back as far as you need to until you see green, living stems. Might be 6".... might need to go down to 2-3" above the crown of the plant. Do this to the entire plant. Move the plant to an area of less direct sun & less heat for awhile.

Water lightly every 2-3 days depending upon heat. Check the dampness of the soil, around the roots ... below surface level.

You will see new growth, and it will begin to revive. It will actually be stronger than before. Be patient! When it gets to be REALLY BIG, you can also cut it back hard after it's flowering season. Ready to repot in a couple of years.

The key is for YOU to control the elements, and the environment. GOOD LUCK!!!!