The Webster's article is lie (intrans., in the sense of rest) vs. lay (trans., in the sense of place). Ie "I lie on the couch = I rest on the couch" vs. "I lay my baby in the bed = I place my baby in the bed". It has nothing to do with lie in the sense of telling untruths.
Websters seems to argue both sides!
Not at all. They tell you the prescriptive grammar rule, and the descriptive grammar rule and discuss whether the prescriptive rule will ever be changed to fall into line with the descriptive rule.
But if it does rise to respectability, it is sure to do so slowly: many people have invested effort in learning to keep lie and lay distinct.
Even if intransitive lay rises to respectability that will not make the older intransitive lie wrong. You corrected accepted (correct) usage to the controversial (wrong) usage.
In grade school, I was taught that 'lie' should be used for 'untruths' and 'lay' should be used for 'position' or 'proximity'.
I think you should sue your grade school. :-) They taught you something that "others will judge you unfavorably" for (to quote Websters).
The 'correct' prescriptive grammar rule is that:
Lie (past tense lay) is for proximity or position
Lay (past tense laid) is something you do to something/someone/yourself
Lie (past tense lied) is to tell an untruth
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