Meanings of "in the sense that" [closed]

Solution 1:

"In the sense that" is correctly used to distinguish between two possible senses (approximately meanings) of a word or phrase. So:

"This fact is funny, in the sense that it makes me laugh"

or

"This fact is funny, in the sense that it is strange".

So to take your third example, "lost" can mean a number of things, including "irretrievable" and "destroyed", and in this case it means the first.

Solution 2:

"In the sense that" is an idiomatic shorthand for "because".
Example:
[This is] screwy [because] two of college basketball's most historic programs are playing for a national title game and it's blowing people's minds.

"It the sense that", is a linking phrase that implies causality between the subject and the predicate, but it does so in a softer, more indirect (more formal?) manner than just saying because.
For instance:
"This homework essay is terrible because it doesn't make a valid argument."
This can be accusatory and harsh.
"This homework essay is terrible in the sense that it doesn't make a valid argument."
This seems softer, more polite, and less accusative.

It can also call attention to a certain sub-element of the subject.
"This homework essay is terrible because it doesn't make a valid argument."
This could imply that the homework is terrible in totality. Because it doesn't make a valid argument, it is Completely Wrong.
"This homework essay is terrible in the sense that it doesn't make a valid argument."
This could imply that the homework is terrible, but only partially. Specifically, the failure to make a valid argument (a portion of the subject homework essay) makes it terrible, but it doesn't condemn the other portions of the subject.