Rhodes-Vivour was on Wednesday, declared winner of the LP substitution primary, which took place at Ikeja, Lagos.
He polled 111 votes to defeat Moshood Salvador, a former chieftain of the All Progressives Congress (APC), who got 102 votes.
Announcing the results, Bashiru Apapa, deputy national chairman of LP, declared Rhodes-Vivour as the winner of the exercise.
A substitution primary is conducted if the candidate for an elective position withdraws from the race, becomes incapacitated, or dies before the election.
In the acceptance speech, Rhodes-Vivour said his victory is the first step to take over Lagos from the All Progressives Congress (APC).
On his part, Salvador rejected the outcome of the election, alleging that some delegates who voted were not meant to participate in the primary.