We analyze the degree reverse lexicographic generic initial ideals of locally CohenMacaulay space curves and how they behave under biliaison. We provide a complete classification for both general members of componenets of the locally CohenMacaulay Hilbert scheme of degree three space curves for each genus and lower triangle diagrams with only one non-zero entry after a general change of coordinates. We also consider curves where a general hyperplane section has the same Hilbert function as a general hyperplane section of an extremal curve, giving special consideration to curves in double planes. We resolve the ideals of curves in double planes and give a symmetry condition on their triangle diagrams.