Answer:
Lets be clear, in an inertial frame of reference it will take 1 newton to move 1 kilogram 1 meter in one second(roughly). 1 joule in that newton, 1/speed of light = incremental mass increase( irrelevant) . So, to move 1 kg of mass 1 meter in 0.00000003 seconds would take 300,000,000 joules(fun).
That divided by speed of light again and your 1kg mass is now 2 kg. Now to move 2 kg 1 meter would take more energy than previously. More energy (newtons) the more relativistic mass gained and thus more energy required to move faster. This is why we cant reach the speed of light - infinite energy. ( again irrelevent to the Question).
But in your question you said lift. Lift is a term that I would find on earth, in a gravity well, so moving that same 1kg of mass wouldn't take 1 newton because the gravitational force pulls the mass down, causing a force called weight - this would be 9.8 N x Mass at sea level. So to lift this 1kg mass will take more than 9.8 N. 10 newtons of life would create a net force of 0.2 N so 0.2/1 = 0.2 meters acceleration.
Note that, gravitational force is one side of the same coin, with acceleration on the other. We talk of gravitation in terms of acceleration, as two masses that are not identical will always fall at the same acceleration. Gravity isn't a force, its a four dimensional field that curves linear paths toward attracting bodies - this is how we are able to orbit objects in space.