Monte Carlo simulations of the full, i.e. nontruncated, 3d Lennard-Jones fluid in the critical region are reported. The simulations are performed within the grand canonical ensemble in conjunction with hyperspherical boundary conditions in order to take account of the algebraic attractive part of the pair potential. Using mixed-field finite size scaling analysis and with the assumption of Ising criticality the critical temperature is estimated to be T*=1.326+/-0.002 and the critical density rho*=0.316+/-0.002. Precised estimates of the critical energy per unit volume, pressure, chemical potential, and mixed-field parameters are also reported. The values obtained for the renormalization exponents y(tau) and y(h) are compatible with the 3d Ising values within the error bars.