Warren W. answered 03/28/19
I am an ESL instructor who enjoys helping students make more money.
Okay, so, "if you know London so well, you shouldn't have got so hopelessly lost."
Short answer: It can be used, but maybe you shouldn't.
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The trouble with the sentence is that it is awkward. I feel like I am reading Madame Bovary. My assumption is that is why the author minimized its situational use. Besides, I am not sure if this is a completed action i.e. we are lost, yet the sentence uses 'have got so hopelessly lost." Why? I am unsure. Seems like the past participle 'gotten' should be used as in 'have gotten so hopelessly lost'.
If you knew London so well, you shouldn't have gotten so hopelessly lost.
Furthermore, hopelessly? Is that even necessary? Seems dramatic. Avoid drama.
Hope this helps. ~W

Ellen W.
This is a mixed conditional because it includes a present verb phrase with a past verb phrase to talk about an unreal situation. If you know London so well (present) / you shouldn't have got so hopelessly lost (past). But the reality is that you don't know London very well so you got lost. As Warren also mentioned, "Have got" also sounds strange. However, this is a matter of style as "have got" is the dominant usage in UK English but "have gotten" is dominant in US English.05/21/20