The lanthanide orthoborates, LnBO(3), Ln = Gd, Tb, Dy, Ho, Er, Yb crystallise in a monoclinic structure with the magnetic Ln(3+) forming an edge-sharing triangular lattice. The triangles are scalene, however all deviations from the ideal equilateral geometry are less than 1.5%. The bulk magnetic properties are studied using magnetic susceptibility, specific heat and isothermal magnetisation measurements. Heat capacity measurements show ordering features at T <= 2 K for Ln = Gd, Tb, Dy, Er. No ordering is observed for YbBO3 at T >= 0.4 K and HoBO3 is proposed to have a non-magnetic singlet state. Isothermal magnetisation measurements indicate isotropic Gd3+ spins and strong single-ion anisotropy for the other Ln(3+). The change in magnetic entropy has been evaluated to determine the magnetocaloric effect in these materials. GdBO3 and DyBO3 are found to be competitive magnetocaloric materials in the liquid helium temperature regime.