You can replace the first instance of or in the sentence
If a Partner shall retire or die or become permanently disabled or incompetent he shall be released from this lease.
with a comma and not run into any trouble with the parallelism of the sentence. But if you simply replace the second or with a comma, you create a mismatch in parallelism.
What the 'or's mean
As written, the sentence has three parallel branches that sprout from the trunk "shall": retire; die; and become permanently disabled or incompetent. In addition, there is a second (and more ambiguous set of two secondary branches that sprout either from the branch become or the branch permanently, though it's impossible to tell which.
So spelled out in full, the sentence would read either like this:
If a Partner shall retire or die or become permanently disabled or become incompetent, he shall be released from this lease.
or like this:
If a Partner shall retire or die or become permanently disabled or become permanently incompetent, he shall be released from this lease.
But if you render the sentence as
If a Partner shall retire, die, become permanently disabled or incompetent, he shall be released from this lease.
you create a parallel structure with four branches attaching to shall: retire; die; become permanently disabled; and incompetent. One of these branches is not like the others—namely, incompetent, which needs either "become" or "become permanently" added to it in order for it to match the parallel structure of the other three branches.
Shorter but still unambiguous
You can avoid some of the repetition in the two fully-spelled-out versions of the sentence by using commas. Either
If a Partner shall retire, die, become permanently disabled, or become incompetent, he shall be released from this lease.
for the case where the incompetence need not be permanent, or
If a Partner shall retire, die, become permanently disabled, or become permanently incompetent, he shall be released from this lease.
for the case where the incompetence must be permanent (which might be an interesting challenge to have to prove in court).
If you were willing to retain the ambiguity of the original wording with regard to whether the Partner's incompetence need be permanent or not in order to justify breaking the lease, you could use this form:
If a Partner shall retire, die, or become permanently disabled or become incompetent, he shall be released from this lease.
But really, a lawyer should be more careful about spelling out the conditions and exemptions in a contract than the one whose work you are quoting from seems to have been.
How permanent is retirement?
Your question (as I understand it) about whether retirement under the terms of the contract must be permanent in order to satisfy the conditions established for legally breaking the lease opens a different can of worms. The word permanently in the quoted sentence applies unmistakably to "disabled" and arguably (but also arguably not) to "incompetent"; but grammatically it most certainly does not apply to "retire" or to "die."
As the other answerers point out, dying is usually permanent (except in The Princess Bride), so the inapplicability of permanently to "die" is of no consequence; but "retired" is a far less fixed status than "dead." If I were arguing against the lease-breaking Partner in court, I would not claim that the lease terms stipulated permanent retirement as a condition for validly breaking the lease—since they clearly don't—but I would assert that the Partner's "temporary retirement" was in fact a sham retirement—that is, no retirement at all, as the word retirement is generally understood, but something in the nature of a "gap year" or "sabbatical."
In the ensuing litigation, depending on how much money the various parties to the dispute had to burn, I would expect all of the lawyers involved in the case to do significantly better than break even, and all signatories to the lease to do significantly worse.