Lorelai is eating a sandwich and watching TV when her labour pains begin. We know it’s a pepper sandwich (I think this means a bell pepper or capsicum sandwich, which sounds weird?), because it was mentioned in an earlier episode. There is a cut, and then we see her at the hospital registry, filling out forms on her own.
She has come to the hospital by herself (presumably in a taxi) and there’s nobody to help her with the paperwork or offer support, not even Christopher. To add poignancy to this, there is a young man standing behind Lorelai with a bunch of flowers for someone, but there is nothing for Lorelai.