Hello Sara Gupta 

No, even if you are holding the state quota getting into LMNIT wtih 56K rank is quite not possible specially for general category students.

Even the lower branches in LMNIT ends somewhere arounf 30K. So, getting LMNIT with 56K rank is quoite not possible.

But you can rty for other lower branches in some Lower NITs or can go for the private engineering colleges like PEC or Thapar, they are not a bad option with this rank.

Hope that helps!