The user may adjust the value, but only downward?
I’m guessing the column in question is Quantity, and that your formula:
[__THIS] < [__THISROW].[Quantity]
is an attempt to compare the user-adjusted value ([__THIS]) against the initial value upon entering the form ([__THISROW].[Quantity]).
(Note that I’ve doubled the underscores in front of THIS and THISROW to avoid formatting problems with Google+. Remove the second underscore in practice.)
You’re on the right track thinking you have to refer to the initial value in some different way, but [__THISROW].[Quantity] and [__THIS] in fact refer to the same value: the copy of the column value the form is using. Your expression is exactly equivalent to [__THIS] < [__THIS]. The specific reason your inputs are always invalid is because you Valid_If insists that the Quantity input must always be less than itself, which is always false.
To get the initial value of the column, you have to tell AppSheet to look at the table by using a function that pulls values from tables, like LOOKUP() or SELECT():
[__THIS] < LOOKUP([__THISROW], “MyTable”, “KeyColumn”, “Quantity”)
[__THIS] < ANY(SELECT(MyTable[Quantity], ([KeyColumn] = [__THISROW])))