The response of the superconducting state and crystal structure of LiFeAs to chemical substitutions on both the Li and the Fe sites has been probed using high-resolution X-ray and neutron diffraction measurements, magnetometry, and muon-spin rotation spectroscopy. The superconductivity is extremely sensitive to composition: Li-deficient materials (Li1-yFe1+yAs with Fe substituting for Li) show a very rapid suppression of the superconducting state, which is destroyed when y exceeds 0.02, echoing the behavior of the Fe1+ySe system. Substitution of Fe by small amounts of Co or Ni results in monotonic lowering of the superconducting transition temperature, T-c, and the superfluid stiffness, rho(s), as the electron count increases. T-c is lowered monotonically at a rate of 10 K per 0.1 electrons added per formula unit irrespective of whether the dopant is Co and Ni, and at higher doping levels superconductivity is completely suppressed. These results and the demonstration that the superfluid stiffness in these LiFeAs-derived compounds is higher than in all of the iron pnictide materials underlines the unique position that LiFeAs occupies in this class.