Context : Aims : We present a study of the orbits of the triple system LHS 1070 , with the aim to determine individual masses of its components . Methods : Sixteen new relative astrometric positions of the three components in the K band were obtained with NACO at the VLT , Omega CASS at the 3.5 m telescope on Calar Alto , and other high-spatial-resolution instruments . We combine them with data from the literature and fit orbit models to the dataset . We derive an improved fit for the orbit of LHS 1070 B and C around each other , and an estimate for the orbit of B and C around A . Results : The orbits are nearly coplanar , with a misalignment angle of less than 10 ^ { \circ } . The masses of the three components are M _ { A } = 0.13 \ldots 0.16 M _ { \odot } , M _ { B } = 0.077 \pm 0.005 M _ { \odot } , and M _ { C } = 0.071 \pm 0.004 M _ { \odot } . Therefore , LHS 1070 C is certainly , and LHS 1070 B probably a brown dwarf . Comparison with theoretical isochrones shows that LHS 1070 A is either fainter or more massive than expected . One possible explanation would be that it is a binary . However , the close companion reported previously could not be confirmed . Conclusions :