"lo siento" is regularly use to show empathy: -A:mi padre murió la semana pasada( my dad passed away last week) -B: oh! I'm so sorry.(oh! lo siento mucho) NEVER--->discúlpeme,perdóneme. "lo siento" "discúlpeme" "perdóneme" the three of them may be interchangable when is about a mistake you make as you learn more spanish you'll see this is not complicated at all when you want to adress someone as "excuseme" use "discúlpe" you can use "perdóne" is ok too. when you didn't hear what someone said "lo siento, no escuche lo que dijiste ¿puedes reptirlo porfavor?"------>I'm sorry, I didn't hear what you said could you repeat it please?

All are the same if what you want is to apologize, you can use them in different ways, that "way" is what determines if it's or not formal. Todos son lo mismo si lo que quieres es disculparte, puedes usarlos de distintas materas, esa "manera" es lo que determina si es o no formal. For example "discúlpeme" is more formal than "discúlpe", and "discúlpe" is more formal than "discúlpa". Por ejemplo "discúlpeme" es más formal que "discúlpe" y "discúlpe" es más formal que "disculpa". And never forget the intonation, it's very important cause any of the words could be rude or polite depending on that. Y nunca olvidar la entonación, es muy importante porque cualquiera de las palabras puede ser grosera o educada dependiendo de eso. Regards. Saludos.

"Perdóneme" and "discúlpeme" are the same: they both mean "forgive me" in a formal way. "Perdóname" and "discúlpame" mean "forgive me" too but in an informal way. "Lo siento" and "lo lamento" mean "I'm sorry". Ojalá te haya ayudado!

The 3 you mentioned means apologize or sorry (are the same).... But.... Can be used as well as excuse me (if you want to ask something to somebody in a shop) and disculpeme and perdoneme are more formal than lo siento... So doesn't matter which one you use to apologize :D