Answering first to what you were told about herir and lastimar:
«Some people believe that one simply is stronger than the other.»
True, in general herir and its related words imply a physical wound, while lastimar might refer to a scratch. Herir tends to be used more in medical/technical speech, where lastimar is a bit more informal, so naturally herir is associated with serious injuries. Note however that you can say Se lastimó mucho al caer and La caída le provocó una herida superficial, which inverts the usual connotations.
«Other people are convinced that one can only be used for physical damage and the other only for emotional damage.»
Not really. Sus palabras me lastimaron is synonym with Sus palabras me hirieron. There's an idiomatic expression, una herida abierta, that can be used figuratively to refer to a deep emotional hurt, in a way where lastimar cannot, but that's it.
«I found another person saying that "lastimar" is very old-fashioned and hardly used anymore and "herir" is the word to use for both types of "to hurt".»
Definitely false. Both words are used, in different contexts to be sure.
- When used informally, herir is usually active: Lo hirieron en la cabeza.
- Lastimar tends to be passive or reflexive, in form or meaning: Me lastimé la mano or Salió muy lastimado de esa relación.
- At least in my dialect (Argentina/Rioplatense) it's not done using herir in the impersonal passive (Se hirió la mano).
- Newspaper headlines do use herir in the passive: Dos personas resultaron heridas or Un guardia de seguridad fue herido durante el asalto al banco.
From herir you have
- herida "wound, cut",
- herido/a (noun) "wounded person, victim with a wound",
- hiriente "hurting, piercing" (figuratively: comentarios hirientes).
From lastimar you have
- lastimadura "slight wound, scratch" and
- lástima "pity" (not semantically close).
If there's an accident, you say there were e. g. tres heridos, or un herido de gravedad. You can't say there are *lastimados.
If something is hurtful, it is hiriente, not *lastimante.