I am not sure if my original post was clear, but my suggestion was to siphon out the sediment and leave the lye solution in your tank. You can siphon out the water into several buckets and then scoop out the sediment, if that is what you'd rather do.
I would skip the filtration step. If your tank has been allowed to sit quiescently for a few days, the water you siphon out should be relatively free of suspended solids, so filtration won't do much good. On the other hand, if you siphon out the sludge, it will quickly blind cheese cloth or other type of filter so the water passes through very slowly. The sludge can be a somewhat gelatinous mess, so be forewarned.
Just to let you know, I have used a lye tank for many years. I have siphoned out sediment a few times, but have never felt that the liquid needed to be filtered.
One last thing, there is an article in the most recent issue of our newsletter, The Casting Call, on the topic of waste disposal.
Jeff