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Share what you know. Learn what you don't.
1. You could swim or sail "on the lake", stressing the fact that you
are on (or near) the surface, whereas "in the lake" could mean wholly
underwater, or could stress being within the perimeter of the lake (not
on the beach). Strangely, "on the lake" can also mean "right next to
the lake", as in "a vacation home on the lake".
2. "I'll lie on the bed" describes your position, without implying
anything about whether you've gotten under the covers. A midday nap on
top of (not within) the bedclothes would be likely termed "on the bed".
3. A "child asleep in the bed" has likely been "tucked in", and is
in/under the bedclothes. (Also, we cannot ignore the psychological
factor that the parent probably wants the kid to stay put, and "in"
sounds more confining.)
--
Jack Gavin
'On' in the first sentence sounds slightly odd to me -- I would use 'in'.
You might go sailing or skiing 'on' a lake, but you swim 'in' it.
For the other two, 'on' means lying uncovered on top of the bed , 'in'
means underneath the bed-covers, blankets or whatever.
Regards,
John.