What's the context? Why are you asking?
The difference is quite significant, IMHO.
1. The meaning:
Lest:
1. With the intention of preventing (something undesirable); to avoid the risk of.
‘he spent whole days in his room, wearing headphones lest he disturb anyone’
More example sentences
1.1(after a clause indicating fear) because of the possibility of something undesirable happening; in case.
‘she sat up late worrying lest he be murdered on the way home’
(https://en.oxforddictionaries.com/definition/lest)
'in case' = In the event of (a particular situation) (https://en.oxforddictionaries.com/definition/in_case_of)
2. 'lest' is formal, 'in case'' is not
3. 'lest' always requires Subjunctive:
There are very few contexts in English where the subjunctive mood is, strictly speaking, required: lest remains one of them. Thus the standard use is she was worrying lest he be attacked (not lest he was …) or she is using headphones lest she disturb anyone (not … lest she disturbs anyone). (https://en.oxforddictionaries.com/definition/lest),
I hope it helps
October 12, 2016
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