"Less" can be a determiner and a pronoun (less time), an adverb (less pretty), or a preposition (the original price less 10% discount = minus), used to be an adjective as well but is not any more in modern language.
"Lack" can be a noun (a lack of confidence) or a verb (the hospital lacks parking spaces).
You can use "less" to compare the amounts of uncountable things (meaning there's not "as much" of something) or the degree (this road is not "as" busy, it's less busy). "Lack" means that there isn't enough of something. It is not about physical vs emotional. You can have less patience = you lack patience = your lack of patience is...