If there is no law in your state to make taxing authorities “properly” value properties, you have nothing to hold anyone accountable to follow.
This whole issue is only on you, unless you change the law or follow the expected process to protest the valuation.
You, in fact, are even lying when you claim the tax appraiser is “lying,” as you do in your title.
I live in Texas -— my Father lived in New Mexico.
I’m shocked by the government boot licking on this thread. A property in disrepair had its taxable value improperly increased each year by a dishonest government drone and you want to blame the victim. Should the elderly property owner have fought the bogus valuation, sure, but that does not mean the lazy lying tax assessor was in the right. Disgusting.