If the suspended Brother was suspended for anything other then NPD (non-payment of dues) then not even a vote is required as long as he has not been suspended for more that 3 years. Then an investigation is required and a ballot taken.
See Chaper 18 in the GLoTX Law Book
Art. 327. (363). Expulsion Permitted After Three Years:
Reinstatement. When a member of a Lodge has been expelled for
the non-payment of his dues as provided in Art. 326, and desires
to be reinstated to membership, he shall present such a petition
to his Lodge, in writing, at a stated meeting thereof, and pay all
dues in arrears, up to the date of his suspension, unless same has
been reduced as authorized by Art. 314 of the Laws, in which case
the amount authorized shall be paid. The petition shall lay over
to a subsequent stated meeting and the Worshipful Master shall
appoint a committee for investigation and report. It shall require
a unanimous favorable ballot of the members of such Lodge present
to reinstate the petitioner to membership. If such petitioner is
rejected he may petition for reinstatement again after six months
have elapsed. If he is rejected a second time he shall not petition
again until one year has elapsed from the date of the last rejection.
Any subsequent petitions shall not be received except after the
elapse of an additional year. Any such petitioner for reinstatement,
who is rejected, shall, upon demand, be entitled to a refund of the
dues so paid.