Interleukin 6 class cytokines
From the interleukin wikipedia page for IL6 :


  number of other cytokines may be grouped with IL6 on the basis of sequence    similarity.[21][22][23] These include granulocyte colony-stimulating factor (GCSF) and myelomonocytic growth factor (MGF)


from the Leukemia inhibitory factor wikipedia page:


  LIF derives its name from its ability to induce the terminal
  differentiation of myeloid leukemic cells, thus preventing their
  continued growth.


From this we can suggest that LIF is grouped with the IL6 because of its action on myeloid leukemic cells and specifically on their growth (MGF).