"I have found the key"
Can it mean in a context that
"I lost my key. I have found the key in an unspecified time in the past (it isn't interesting) but now I actually don't know where it is, maybe I lost sometime ago or somewhere else?
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No, as stated, I have found the key, without further qualification, would not mean that you do not know where it is now, that it has perhaps become lost yet again. It means that you have in your possession the key you have been looking for. In practical contexts, listeners typically eliminate remote possibilities and opt for the salient, most probable meaning.
You would need to qualify the statement if you wanted it to mean—if you wanted your listener to understand— that finding the key is something you've done in the past from time to time, not that the key is presently in your possession; here's a scenario:
I have found that key many times. I keep losing it, and I've lost it yet again.
P.S. find is different from live and eat in that find is a verb with an end or goal, whereas those other verbs do not have a completion sense. I have eaten at that restaurant and I have lived in London., as you say, do not mean I have just come from that restaurant where I was eating a moment ago, or I have just come from London, where I had been living up until a moment ago. However, I have found the key or I have boiled the water do indeed mean that you have just done those things a moment ago. That is in part because of the use of the definite article, the.
If you wanted to say that you know how to boil water, you would discard the definite article, the, while keeping the same tense:
I have boiled water. I have done it in my life. I know how to do it.
I have boiled the water. I did it a moment ago. The pasta can go into the pot now.
With key it is not as easy, since we cannot say:
I have found key. ungrammatical
If you wanted to say that you know how to find a lost key, that you are an excellent searcher for lost items, you can use the plural instead:
I have found keys.
I have found a key or two in my day.
Or if you mean that specific key, you would need to add a time phrase to make your meaning clear, as I mentioned above:
I have found that key before.
I have found that key from time to time.
I have lost and found that key so many times.
Absent such qualifiers, "I have found that key" would be understood to mean "That key I have been looking for -- I have it now."