I don't know too much about it. I've never used it in soap. From my reading --
It has been used as an inexpensive filler in soap -- in effect, it allows the soap maker to produce a decent-looking hard soap with a higher than normal water content. Water is cheap, so the cost to make the soap is reduced.
Like any salt, sodium silicate will tend to harden bar soap. It adds detergency (cleaning power) to the soap, which is why it is used in laundry detergents. It will soften hard water to some extent depending on the amount used.
It may consume lye especially if the soap is made at higher temperatures -- I don't have any advice on adjusting the NaOH amount. It can crystallize out of the soap if too much is used in a bar (NaOH) or liquid (KOH) soap.
As far as safety for use on the skin -- no idea. As far as how it compares to sodium lactate -- again, no idea.