First-principles calculations reveal the effects of lead, bismuth and alloying elements (M=Al, Si, V, Cr, Mn, Ni, Nb and Mo) on thermodynamic stability, elastic properties, elastic anisotropy and fracture toughness of alpha-Fe. Overall, Pb and Bi increase the elastic anisotropy of iron, and reduce the thermodynamic stability, elastic properties and fracture toughness of iron, but alloying elements have little effect on these properties of iron without liquid lead-bismuth eutectic (LBE). Moreover, V, Mn and Nb can hinder the influence from Pb and Bi on iron, while Al, Si, Cr, Ni and Mo would exacerbate these effects. Combined with the plastic dissipation coefficient, the calculations also show that Fe first breaks along the (100) plane, followed by the (110) plane in all cases, while the (111) and (112) planes are hard to crack. And it is also found that the elastic properties of Fe play an important role at its fracture toughness. In addition, a clear functional relationship between fracture toughness and elastic anisotropy is proposed, which provides a deep understanding of liquid metal embrittlement (LME) of iron in lead-bismuth eutectic. The obtained results are in good agreement with experimental measurements in the literature.