The magnetic order in La1.65Eu0.20Sr0.15CuO4 has been studied under external pressure p≤8.3kbar by means of zero field and transversal field muon spin relaxation. At ambient pressure this system is in the LTT structure and exhibits static spin stripe order below 25K as evidenced by a spontaneous muon spin precession. Applying hydrostatic pressure the magnetic transition temperature as well as the sublattice magnetization and the magnetic volume fraction are reduced. Since external pressure also reduces the LTT tilt angle these experiments prove that the stability of the static stripe phase is strongly coupled to the LTT structure in this system.