It's not that uncommon to have pumps to drain waste water UP to the outlet, even toilets (toilets require a different type of pump). For example, in our lakehouse, we have a basement sink that drains into a sump hole. From there, it's pumped up to the main drain where it flows into the septic system. I will say that building codes in that location are not as stringent as in many cities.
Any sump pump should work, though I can't say how it will stand up to chemicals. You should make sure that you install a checkvalve. The sump pump would need to be sized so that it won't be overwhelmed by the water supply.
But I infer from your post that there is no sump hole, raising the question of how you would mount the pump. Is that the case?