Why is it necessary to burn the hydrogen fuel coming out of the engine for the lift of the rockets ?
Hydrogen isn't the only fuel possible, so I presume your question is more general, why is any fuel burned?
If it is done to create a greater reaction force on the rocket then why can't we do the same lift with just adjusting the speed of the hydrogen gas going out of the engine like we can release them at a great pressure and thus at a greater speed?
You need two things for a rocket: a reaction mass to expel, and a source of power to accelerate it. Combustion rockets combine these two into a single source. The fuel/oxidizer burns generating energy. The energy from combustion heats and then, via the nozzle configuration, accelerates the combustion products as the reaction mass.
Just about anything could be put onboard as the reaction mass, but getting the power to accelerate it is much harder. Batteries and compressed gas hold a bit of energy, but the density is much lower than rocket fuels. Solar panels can gather a nearly unlimited amount of energy, but you have to wait for a long time to collect it. Nuclear fuels could release a lot of power, but putting a nuclear reactor on a rocket takes a lot of mass and is difficult to convince everyone that it can be done safely.
Even if you had sufficient electrical power, converting it into thrust isn't simple. Ion engines can be used, but they have orders of magnitude less thrust than a chemical rocket. The acceleration can be useful in space, but is too small to help lift a rocket off the surface of the earth.
So the fuel is burned because it can be stored on the rocket with a fairly high energy density, and the reaction can take place at a high rate, giving large amounts of thrust.