What is the difference between the neuter lo and the object pronoun lo?

They are spelt the same but do different jobs. The object pronoun lo replaces a masculine or neuter direct object - ¿Ves el coche? Sí, lo veo (Do you see the car? Yes, I see it). The neuter article lo sits in front of an adjective, adverb or relative to build an abstract idea - lo bueno (the good thing), lo que dijo (what he said). If lo is standing in for a noun already mentioned, it is the pronoun; if it is creating an abstract 'the ... thing / what ...', it is the neuter article.

How does lo + adjective work?

lo plus a masculine-singular adjective makes an abstract noun meaning 'the ... thing' or 'the ... part': lo bueno (the good thing), lo difícil (the hard part), lo importante (the important thing), lo mejor (the best thing). The adjective stays masculine singular no matter what, because lo has no gender or number - it is never 'la buena' or 'los buenos' in this use. You can extend it: lo bueno de vivir aquí (the good thing about living here), lo más importante (the most important thing).

What does lo que mean?

lo que is the relative 'what' in the sense of 'that which' - it refers to a whole idea rather than a named noun. No entiendo lo que dices (I don't understand what you say). It also sums up a previous clause: llegó tarde, lo que me molestó (he arrived late, which annoyed me) - here lo que (or lo cual) means 'a fact which'. Do not confuse it with qué (with an accent), which asks a question: ¿Qué dices? (What are you saying?) versus no oí lo que dijiste (I didn't hear what you said).

The Neuter lo

There are two little words spelt lo in Spanish, and they are easy to mix up. One is the object pronoun - lo veo, I see it/him. The other, the subject of this page, is the neuter article lo: a genderless, numberless word that turns adjectives and clauses into abstract ideas. Lo bueno is "the good thing"; lo que dijo is "what he said". English has no single word for it, which is exactly why it needs practice.

The key fact: the neuter lo is invariable. It never becomes la, los or las, because it does not point at a thing with a gender - it points at a concept. Keep that in mind and its four patterns fall into place.

1. lo + adjective: the abstract noun

Put lo in front of a masculine singular adjective and you get an abstract noun meaning "the ... thing" or "the ... part".

lo bueno - the good thing / the good part
lo malo - the bad thing
lo importante - the important thing
lo difícil - the hard part
lo mejor / lo peor - the best / worst thing

The adjective stays masculine singular whatever the context, because lo has no gender:

Lo bueno es que ya terminamos. (The good thing is that we've finished.)
Lo difícil fue empezar. (The hard part was starting.)
Haz lo posible. (Do what you can / the possible.)

You can stretch it with de or a superlative:

lo bueno de vivir aquí (the good thing about living here)
lo más importante (the most important thing)
lo mejor de la película (the best bit of the film)

This also works with possessives - lo mío (what's mine / my business), lo nuestro (what we have between us) - always neuter, always singular.

2. lo + adjective/adverb + que: measuring degree

Lo teams up with que to measure how something is - the "how + adjective" exclamation. Here the adjective agrees with what it describes (this is the one case where it can), but lo itself never changes.

No sabes lo difícil que fue. (You have no idea how hard it was.)
Mira lo altos que están tus hijos. (Look how tall your children are.) - altos agrees, plural masculine.
Me sorprende lo bien que habla. (I'm amazed at how well she speaks.) - with an adverb, bien.
Con lo cara que es, no la compro. (Given how expensive it is, I'm not buying it.)

The pattern is lo + adjective/adverb + que + verb and it packs the English "how ... it is" into three words.

3. lo que / lo cual: the relative "what" and "which"

Lo que is the relative pronoun for a whole idea rather than a named noun - English "what" in the sense of "that which".

No entiendo lo que dices. (I don't understand what you say.)
Haz lo que quieras. (Do what you want.)
Lo que necesito es tiempo. (What I need is time.)

When it refers back to a whole previous clause - "a fact which" - both lo que and the more formal lo cual work:

Llegó tarde, lo que (lo cual) me molestó. (He arrived late, which annoyed me.)
No contestó, lo cual me preocupó. (He didn't answer, which worried me.)

Keep it apart from the interrogative qué (with an accent), which asks a direct or indirect question: ¿Qué dices? (What are you saying?) but no oí lo que dijiste (I didn't hear what you said). Question = qué; "that which" = lo que.

4. lo de: the matter of

Lo de plus a noun, name or infinitive means "the matter of", "the business about", "that thing with" - a handy way to refer to a known affair without spelling it out.

¿Sabes lo de Pedro? (Have you heard the thing about Pedro?)
Lo de ayer fue un error. (That business yesterday was a mistake.)
Olvida lo de la fiesta. (Forget the whole party thing.)
Lo de trabajar los domingos no me gusta. (This working-on-Sundays thing, I don't like it.)

It is casual, extremely common, and neatly vague - which is often the point.

Worked examples

Lo mejor de todo fue el final. (The best thing of all was the ending.) - lo + adjective.
No te imaginas lo cansado que estoy. (You can't imagine how tired I am.) - lo... que.
Lo que más me gusta es cocinar. (What I like most is cooking.) - lo que, relative.
Se fue sin avisar, lo cual me pareció grosero. (He left without a word, which struck me as rude.) - lo cual summing up a clause.
Tenemos que hablar de lo de tu hermano. (We need to talk about the thing with your brother.) - lo de.
Lo importante no es ganar. (The important thing isn't winning.) - lo + adjective as subject.

Common mistakes English speakers make

Making lo agree. The neuter lo never changes: it is lo bueno, never "la buena" or "los buenos", even when the idea feels feminine or plural. Agreement would turn it back into an ordinary article + noun.

Using el que for an abstract 'what'. For "what" meaning "that which" over a whole idea, it is lo que, not el que or la que (those refer to specific gendered nouns: el que llegó, the one who arrived). Lo que necesito, not "el que necesito", for "what I need".

Confusing lo que with qué. The question word carries an accent - ¿qué? - and the relative does not - lo que. "I know what you want" is sé lo que quieres; "what do you want?" is ¿qué quieres?.

Forgetting the adjective can agree in lo... que. In lo altos que están, the adjective altos agrees with the children even though lo does not. Leaving it as "lo alto que están" is a common slip.

Two words, one spelling. When lo stands in for a thing already named, it is the pronoun; when it builds "the ... thing", "how ...", "what ..." or "the matter of", it is the neuter article - invariable, abstract, and everywhere in real Spanish.