I'm pretty sure Lex doesn't consider it, but I'd have to reread it to make sure. My memory is that Lex just looks at the risk of of Superman becoming dangerous, which is fairly low, and considers that the amount of damage Superman could do is so high that drastic measures must be taken. IIRC, Lex never finds out how very non-human Superman is, so I can't blame him for not updating on the risk of mental problems.
I'm more certain that Lex never considers the possibility that if Superman exists, then so might other aliens, so Superman might be needed to defend the earth from alien attack.
No, he definitely takes seriously the mental concerns seriously. Consider https://www.fanfiction.net/s/10360716/4/The-Metropolitan-Man :
...Superman was an extinction level event waiting to happen, and where those were concerned there were no second chances. If Superman ever decided to kill everyone, there would be no stopping him, and so it stood to reason that humanity should take every possible precaution to prevent that from happening. The most direct path would be through killing Superman. Lex had written multiple letters to the editor under various pse
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