What is Aristophanes trying to say about the importance of marriage to the state when he shows the men weakened by a lack of marital attention?
First, we need to remember that Lysistrata is a comedy and that unsatisfied male sexual desire was a typical element of Greek comedy. Typical comic actor costumes include a large erect phallus made of red leather, and many of the jokes in Aristophanes and the equally humorous satyr plays make reference to the phallus; some of the jokes were extremely visual in nature, and at times difficult to assess based simply on the texts which have been transmitted without stage directions.
Greek marriage, of which our most detailed account may be found in Xenophon's Oeconomicus, normally involved an adult (approximately 30) man taking a wife just at the beginning of her reproductive age (12-14) for the purpose of trying to father living male offspring in an era of high infant mortality. Greek society was radically homosocial -- men socialized with other men, and women with other women. They often even attended separate religious rituals.
There is no evidence that Aristophanes was unconventional in his notions of women; a proto-feminist reading of the play is probably anachronistic. The importance of marriage was primarily fathering sons to sustain population, in a era in which the Peloponnesian wars were decimating the Athenian male population. Aristophanes' plays consistently oppose the Peloponnesian wars, and like his "Peace", the point of this play is to suggest that Athenians, rather than prosecuting foreign wars, should focus more on cultivating their estates. Marriage was a critical part of household economics, with women providing heirs and also engaging in most of the clothing production of the estate.
Lysistrata and her friends are important vehicles for this argument because Aristophanes is making the point that the Peloponnesian wars are so obviously harming Athens, that even women can see their pointlessness. The sexual strike, of course, is intended mainly for its comic effect.
In Lysistrata Aristophanes is exploring the interdependence of the sexes. The women start out weak and sex-crazed, but once they are organized by Lysistrata, they discover that they have power both over their own destiny and over their husbands' behaviors. Aristophanes' ultimate themes here include the concept that men need love just as much as women, and that marriage can and should be a partnership rather than a master/slave relationship.