"Yo quiero una cosa" And "Yo lo que quiero una cosa" Translate the same And so does " Tu me das lo que quiero" And "Tu me das que yo quiero" Literal translation of lo is 'whatever' So does that mean that we can skip lo and transform a sentence in some other way like we do in English?
«Yo lo que quiero una cosa» is syntactically wrong: the nearest intelligible phrase would be «yo lo que quiero es una cosa». As well, «tu me das que yo quiero» would not be correct without a lo (exempli gratia «tu me das lo que yo quiero»). — By the way: great question!– 0x2b3bfa0Mar 18, 2020 at 20:50
"Yo quiero una cosa" means "I want one thing". "Yo lo que quiero es una cosa" (note the "es": the sentence in your question is not correct) can be reordered to "Lo que yo quiero es una cosa", meaning "What I want is one thing".
"Tú me das lo que quiero" means "You give me what I want". "Tú me das que yo quiero" could be translated as "You give me [the fact] that I want", which is meaningless. I suspect that's not what you meant.
So what's the role of "lo"?
The subordinate clause "que quiero" works like an adjective. You could replace it with "querida por mí", which sounds weird but not wrong. It's the same in English: "the thing that I want", but "that" is usually omitted in English: "the thing I want" (whereas "que" cannot possibly be omitted here in Spanish).
The article "lo" (not to be confused with the pronoun "lo") allows an adjective to work as a noun. For instance, "Lo bueno es pasajero" means "Good things are fleeting". "Lo bueno" is the subject. There is no direct equivalent in English for "lo" in this role.
You can also use "lo" with subordinate clauses that work like an adjective: "Lo que es bueno es pasajero", meaning "That which is good is fleeting". "Lo que es bueno" is the subject.
Therefore, you can't just skip "lo" without changing the whole structure of the sentence.