No, you need KOH to make liquid soap. Grating bar soap and adding water to it will make some sort of liquid, but it will not give you the same results as true liquid soap made from KOH.
Which will give you a "snot" consistency. And if you add enough water to not get the snotty consistency, then what you have is basically a slightly soapy water.
You can, however, make a good liquid soap with a blend of KOH and NaOH.
Be careful of using the term "lye" for NaOH, because "lye" can actually mean either.
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