I'm tired of my lover. How can I break up with them and get a new one?

Solution 1:

According to a Gamefront guide

NOTE: All serious relationships are final! You can only have one romantic relationship. Entering one will nullify others.

It seems like you confirmed this yourself with a missing dialog option.

Solution 2:

According to the romance article the only romances you can actually break up are ones you have previously romanced in either ME1 or ME2

For example, if you bed Ashley in ME1, then Miranda in ME2, then you will be given dialogue choices between the both of them and must decide which one you want to continue with, effectively breaking up with the other. You also have the option of denying both of them and going for one of the newer ones like Cortez or Allers.

(note, answer written assuming male Shepard, see the above linked article for all possible romance options)