Twin suns, along with the dark stars and many moons, are a common element of descriptions of Carcosa. Usually implied to be dim, in common with themes of fading decadence and dying dynasties, they may overlap with the concept of a red sun. According to The Repairer of Reputations, they sink into the lake at sunset; this may simply be a turn of phrase related to line of sight, akin to saying "the sun went down into the sea", but maybe not...
It is possible that this is a reference to the phenomenon known as a sun dog when a second sun appears visible in the sky. For an alternative interpretation of the twin suns falling into a lake, see Fallout and Alchera.
In astronomy, a binary star system is one in which two stars share a mutual central orbit. In a planet orbiting such a system, there would be two "suns" in the sky. If they are the same size, they could arguably be termed "twin suns". The majority of observable stars exist in systems of two or more stars, with single stars (like our Sun) accounting for less than a third of known stars.