Gas production is directly proportional to the current draw only. At STP conditions (0 deg C, 1 atm) you need approximately 1.594 Amps for each LPH per one cell, while you need less if you measure the gas volume at room temperature.
The ideal cell voltage would be about 1.48V, and anything above it is wasted efficiency. The lowest practical cell voltage seems to be around 1.8V-2.0V. The voltage is only needed to push the current thru the cell, it has no relation on the amount of gas produced. The cell overvoltage (above 1.48V) is determined by electrode materials, current density, electrode spacing and conductivity of electrolyte.
Power or total efficiency is defined as the amount of watts needed to produce one LPH. Series-cell designs seem to have the best efficiency in the range of 2.5-3 Watts per LPH. The most efficient electrolyzer would have a large number (100) of cells in series with narrow cell spacing (3mm) at a low current (10A).
Many people build simple single-cell car hydro-booster type electrolyzers and control the amperage by using weak electrolyte. The cell voltage is often around 13V, and they put just enough electrolyte to pass 5A or so. 5A creates only 3.5 LPH of gas, so the efficiency is very bad at 18.5 Watts per LPH. Properly designed 7-cell series electrolyzer would produce 7 times that amount or 24.5 LPH gas at the same input power.
The cell voltage is also dependent on the current density (current / electrode area). Smaller cell area is less efficient because it requires higher voltage to pass the same amount of amps. Good practical current density is around 0.5A/Sq.inch or 0.1A/cm^2. The electrolyzer shown in this report had an effective plate area of about 170cm^2, with a target current of about 20A.