Since you're speaking in generalities, you can use the first person plural pronoun, even if you regard yourself as one of the exceptions (it's assumed that generalities can have exceptions). For example, I might say:
Us men, we never remember our anniversaries.
even if I happen to be a man who always remembers to make a reservation for our anniversary dinner well ahead of time.
I'm talking about men in general, and if I happen to be a man, that's the best way to say it – I should include myself in the first group, since I'm clearly a member of that group.
I suppose I could say:
Those men, they can never remember their anniversaries.
but that seems more fitting for a women to say, not a man. If a man says it that way, he's muddling the conversation, by creating three groups instead of two.
Since these kind of remarks are often intended to be somewhat humorous, we dampen the humor when we get so particular about the pronouns. It's better to be a little self-deprecating and include ourselves with the group, even if we don't exhibit the behavior.
When your friend says:
Indians are the worst drivers, we can take a turn from anywhere!
that's more likely to make me smile or laugh, whle:
Indians are the worst drivers, they can take a turn from anywhere!
sounds more like a peeve or a rant against others in a group that person belongs to, and some of the humor is lost.
As has been said in the comments, languages are constantly undergoing transformation. In cases like this, I like to use Google Ngrams. You can basically search a database of books written after 1900 for specific expressions and their frequency of use.
Link to Ngrams page
As you can see, "by him who" is vastly more popular, so I suggest using that, as @apsillers already stated in a comment.
Best Answer
In formal and scholastic registers, "he" is appropriate. It is part of the subject of the subordinate clause.
The alternatives presented here are that Lily had planned the party and that he had planned the party. The complete subject of the clause is "Lily [and] not he", which excludes the latter alternative.
That being said, the informal registers of many English dialects are not exclusively subject-oriented. For the same reason that the formal "it is I" is often replaced by the common "that's me", the appositive "not him" can easily take the oblique case -- not as an object but merely as a non-topic.
We don't commonly regard English as a topic-oriented language. Still, we can't explain how the informal variants of copular clauses (such as "that's me") and interrogative clauses (such as "who did you see?") function under a purely subject-oriented framework.