As was pointed out in a different thread by 5jj, there's a distinction between someone and anyone:
"Michael Lewis, In
The English Verb (1986.34) sums up the situation rather differently, 'Both some and any are used with indefinite reference. Some is used if the idea is restricted or limited in some way.
Any is used if the idea is unrestricted or unlimited.
[...] the restriction may be a real one [...]or a psychological one existing only in the mind of the speaker.'"
Within the context of sentence 1, he is not interested in what any person at all is doing. That is, there is no restriction placed on whom he is disinterested in, so "anyone" should be used.
In sentence 2, you are instructed not to live a specific other person's life. Because it is restricted to one particular other person's life, one should use "someone."
This can be a fairly nuanced issue to deal with. I hope I was helpful.