The latter. The main driving force in putting the interstitial fluid into the lymphatics is the hydrostatic pressure of the interstitial fluid. If the fluid is drained out of the arteries, but can't be drained via the veins, then interstitial fluid would increase as a result, which would then be drained via the lymphatic system. In that scenario, if the draining capacity of the lymphatics is overwhelmed, then this will be clinically manifested as edema.