Seems like libido is the energy source for mechas in various series such as Star Driver, and Captain Earth. Exactly what is this libido it speaks of? Lust? Why is it that the world will supposedly end if something consumes all libido?
In simple terms, libido is another word used to describe life force, or orgone energy. You can think of it like mana.
Orgone energy is a hypothetical universal life force originally proposed in the 1930s by Wilhelm Reich. -source
To answer your second question (paraphrasing from the source article):
Libido generates orgone energy, so:
No libido -> no orgone energy -> no life.
However the real definition for libido is "sexual desire" which most anime refer to when mentioning the term. So yes lust, so the anime is probably referencing sexual desire or libido as power for their machines.