I've mentioned before that Lily is an object-sexual, but she's not really a typical object-sexual.
Most OSes tend to anthropomorphize the cars or dolls or rollercoasters or landmarks that are the objects of their affection. That way, they can have romances with these things, if not exactly two-way conversations.
Lily, in contrast, actually has no problem with the human form, physically. It's people she can't stand. She's an aromantic object-sexual - that's why the assorted sexdroids of Florenovia are specifically non-sapient, and the women of that setting aren't attracted to each other. That is her paradise. Sex, for Lily, is something you use a thing to do to yourself, for yourself.
And, of course, that is the core of her attitude towards other people's relationships - if sex is something that you use things to do, then, necessarily, having sex with another person (even a lesbian) is the very height of unethical behaviour. It is, by definition, using another person to fulfill your own needs. Sexual and/or romantic relationships are, necessarily, one person utilizing another as either a physical or an emotional tool. At best, a successful relationship would be two people agreeing to use each other in equal measure, like prostitutes who barter to pay for sex with other sex.
Of course, the real kicker about Lily - the reason she's still tolerated by her friends and loathed by certain contingents of my audience - is that nothing she says is ever definitively wrong. Her definitions of relationships and monogamy are not incorrect. Her description of testosterone affecting the brain is not incorrect. Like Max, she starts from a few precepts and simply takes things to their furthest extreme.
Occasionally, though, she does go further than her friends will tolerate.