Oh the horror! The Humanity!!!!
Let’s cut to the chase: Given a reasonably normal relationship*, i.e. no abuse, your husband keeps a job, hasn’t turned into a fat slob, no addictions - if you are denying your husband sex - and you’re refusing to do anything* about your low libido (Visit a doctor, counselling, oh, TALK TO HIM) then you are being sexually manipulative.
Your husband will come to accept this, and 99 times out of a hundred he will seek his relief elsewhere.
And if he does, you deserve to be cheated on. And if he winds up leaving you for her, you deserve that too.
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*Read the italicized. If you jump in with a “what if” based on an abnormal relationship, or someone who is trying to do something about it, it is proof you are an idiot who fails to read thoroughly.