Okieng,
The separator tank will need to be 5 m higher than the drain outlet, as described by quark, for a drain to atmospheric pressure during continuous operation of the vacuum exhauster. It seems the second floor mezzanine does not give you nearly enough height for water head to overcome the partial vacuum of separator tank.
If you could accept intermittent drain operation for low volumes of drain flow, then a "vacuum lock" chamber with three (actuated?) valves could allow draining from the separator tank with less height.
A "vacuum lock" chamber would function like the airlock doors between buildings with a controlled atmosphere, or the docking passage way between space vehicles connecting while in the vacuum of space orbit. A block valve, a drain valve, and a vent valve together on a length of piping would form the vacuum lock chamber. The drain and vent valves would be closed while the block valve remained open to fill the chamber with drainage from the mist elimination separator tank. When the chamber is to be drained, the block valve would first be closed, then the vent and the drain outlet valve would be opened. The block valve and the vent valve might be combined into a 3-way valve to prevent reverse flow if block valve was opened in error. The pipe could be run in horizontal, but it would drain better if oriented vertically. The available height will have to determine the design along with the required volume for drainage and drain cycle periods. The actuated valves could be sequenced with the cleaning showers.
If there is large volume of drainage to be sent to a waste treatment header (instead of process sewer / floor drain) then you might check into the condensate return units from Armstrong or Sarco that use steam pressure to push condensate into condensate collection header piping. Your application would need compressed air to push the fluid to waste treatment header. If the drainage volume is small, but it still needs to be 'pumped' to waste treatment, then consider connecting compressed air to the vent valve of the vacuum lock chamber, and connect vacuum chamber drain valve to the waste treatment header.