Concept problem, we can determine the possible value of Lx in hydrogen

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concept problem, we can determine the possible value of Lx in hydrogen atom?
The book of introduction to quantum mechanics told me that The value of Lx can not be determined.
I know the concept behind this statement
However, when I am practicing, I see one of my question that requires me the determine the possible value of Lx as well as the probability! This is not a homework.
How to determine it? It is possible? The book tell me that Lx can be determined! Is there anything that I am missing?

 

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How is the attachment related to the question?

The book of introduction to quantum mechanics told me that The value of Lx can not be determined.

More context would be interesting.
I guess it is a statement like "if we know Lz, Lx has no fixed unique value".
You can measure Lx, and you will get a result, but then Lz has no longer a fixed unique value.