'lest': How did 'less that' evolve to mean 'for fear that'?

Question

lest, conj. = [OED] Etymology: Old English phrase þý lǽs þe , lit. ‘whereby less’
= Latin quōminus
(þý instrumental of the demonstrative and relative pronoun + lǽs less adj. + þe relative particle). In Middle English the first word of the phrase was dropped,
and les þe became les te in accordance with the general rule that þ after s changed into t.

1.a. [...] = Latin nē, English that..not, for fear that.

[Etymonline] [Similar to Wiktionary's entry]
c. 1200, contracted from Middle English phrase les te "less that,"
from Old English phrase þy læs þe "whereby less that,"
from þy, instrumental case of demonstrative article þæt "that" + læs (see less) + þe "the."
The þy was dropped and the remaining two words contracted into leste.

How should the etymology be interpreted, to understand how "less that"
evolved and drifted semantically to mean:
OED's definition 1a above (that..not, for fear that)?
What semantic drifts connect "less that" with that..not, for fear that?

Answer 1

This usage of lest is learned and clearly modeled after Latin, as your source itself mentions, specifically (timeo) ne (Wiktionary).

In fact, ne can be an adverb or declarative conjunction (like that) of negation, used for instance after verbs of fear to indicate what one fears i.e. hopes not to be. And less is a form of negation just like ne or meno (see https://en.wiktionary.org/wiki/meno#Italian ).