You use 'lo mismo' when you're talking about something neuter, because it's a term to say 'the same thing.' Ej: No me digas lo mismo de nuevo! (Don't tell me the same thing again!) Tenemos que hacer lo mismo que ayer. (We have to do the same thing as yesterday)
But if you specify the object/noun, you use el mismo or la misma. Ej: Vas a llevar la misma falda? (Are you going to wear the same skirt?) Estamos viviendo en el mismo piso. (We are living in the same apartment.)
Not exactly. Never is too strong.
I believe you are correct when there is no referent noun.
Then, "lo mismo" stands alone and means "the same thing".
But if "mismo/misma" refers back to someone or something specific, one uses the definite article for the gender of that person or thing. "El mismo" or "la misma" means "the same" or "the same one".
Please read both "Pronoun" sections of this:
Lo bueno, lo malo y lo feo
» "The good, the bad and the ugly".
To make an adjective into an abstract noun in Spanish lo is used as a neuter definite article before the adjective.
For example, lo importante can be translated as "the important thing," "that which is important," or "what is important." ThoughtCo.com
If the adjective is modifying a noun then the definite article must match the gender of that noun:
La misma edad » "The same age".
I don't know much grammar but I would say Yo haría el mismo trabajo, for example. If you want to say el mismo, I think it would be necessary to put the thing you would do.
the same ~ lo mismo (neutro)
the same work ~ el mismo trabajo (masculino)
the same thing ~ la misma cosa (femenino)
I am not a native English speaker, so I hope my comment makes sense.
I wondered this too. I thought the sentence could potentially be translated either as ..."do it the same" or as "make it the same", and I debated for a moment about which way to translate it, but decided to use "make", which was marked incorrect. It seems to me that hacer is like the French verb faire, which depending on context can be rendered into English as either make or do. In this case we don't really have any context and one could imagine that the verb could mean either do or make.