Solo el presente es lo que se puede controlar.
"Lo" is a pronoun substituting "qué", "the idea/thing" you can control. Think about a possible question:
"¿Qué es "la cosa" (lo) que se puede controlar?
In English, it's the word "what" in "Only the present moment is what you can control."
In the other sentence:
Solo el momento presente es el que puedes controlar.
There is an ellipsis:
Solo el momento presente es el [momento] que puedes controlar.
From all the moments, only the present moment you can control (not the past moment nor the future moment). In English, this is reflected by "the one": "only the present moment is "the one" you can control."
If were talking in general, like in the first sentence (qué se puede controlar):
Solo el momento presente es lo que puedes controlar.
So, it's not about "el que" or "lo que". It's about what substitutions or ellipsis are happening. Depending in the case, it might be "lo" or "el".