The lymphatic system is responsible for transporting interstitial fluid back to the bloodstream, but unlike the cardiovascular system, lacks a centralized pump-the heart-to drive flow. Instead, each collecting lymphatic vessel can individually contract and dilate producing unidirectional flow enforced by intraluminal check valves. Due to the large number and spatial distribution of such pumps, high-level coordination would be unwieldy. This leads to the question of how each segment of lymphatic vessel responds to local signals that can contribute to the coordination of pumping on a network basis. Beginning with elementary fluid mechanics and known cellular behaviors, we show that two complementary oscillators emerge from i) mechanical stretch with calcium ion transport and ii) fluid shear stress induced nitric oxide production (NO). Using numerical simulation and linear stability analysis we show that the newly identified shear-NO oscillator shares similarities with the well-known Van der Pol oscillator, but has unique characteristics. Depending on the operating conditions, the shear-NO process may i) be inherently stable, ii) oscillate spontaneously in response to random disturbances or iii) synchronize with weak periodic stimuli. When the complementary shear-driven and stretch-driven oscillators interact, either may dominate, producing a rich family of behaviors similar to those observed in vivo.