I use a powdered one, don't know what it's called, but my sister uses an orgran one called no egg. From memory I bought mine in the healthy food aisle at the supermarket.

It pretty much works as a binder or thickener, so anything like rissoles, custards, cakes, pikelets etc. I used it for biscuits last year, made one batch with eggs and one without, the batch without were just a teeny bit more crumbley but they held together fine. Can't see why it wouldn't work for lactation cookies.