Relation between the critical density of the universe ($Omega$) and the cosmological constant ($Lambda$) of Einstein's equation

What relation exists between the critical density of the universe indicated by $Omega$ and the cosmological constant $Lambda$ of Einstein’s equation?

Generally with $Omega>1$, $Omega<1$ and $Omega=1$ is considered closed universe, open universe and flat universe respectively.

Often these are also traced back to different astronomical theories as in the example $Omega>1$ which is considered in the Big Crunch model.

Is saying $Omega>1$, $Omega<1$ and $Omega=1$ the same as saying $Lambda>0$, $Lambda<0$ and $Lambda=0$, respectively?