The method by which lymph is pushed through the lymph vessels is via

Contraction of skeletal muscles against the lymph vessel

The lymph usually move in the body in its own vessel and travels from the interstitial spaces to the subclavian veins at the neck area. The lymphatic system does not have a heart to pump and move the fluid. The movement of lymph depends on the movements of the muscles and joints in the body. In this mechanism upward movement is possible. It will move towards the neck where it will be filtered and will go again into the subclavian veins.

Very hard to understand