It's not exactly an origin or first use, but here's the earliest usage I could find.
On being questioned about what was meant, the speaker there expanded by saying "kind of soppy". I agree with the hearer, who replied that this particular metaphorical usage didn't seem very witty or telling.
Having said that, the expression did start to get used more often in the 1980s. Still only a couple of hundred usages in this NGram for there like a lemon, but almost all of them are preceded by some variant of the verbs stand or sit.
In most cases the emphasis is on being kept waiting, with nothing to occupy one's time, rather than OP's implied voluntarily choosing to be idle. The implication being that the subject is unable to do anything about the enforced waiting.
I do not believe this particular usage owes much if anything to the (originally British) slang meaning of a lemon as a poor-quality troublesome purchase (normally a car). Here's the second earliest usage I could find, which again defines the expression in terms of soppiness/ineffectuality. The most common thing done with lemons is to squeeze them; the the metaphorical usage alludes to the fact that we don't expect lemons to resist such treatment.