Only if the lease provides for a rent update
Article 18.1 of the LAU says that, during the lease, rent can only be updated on each anniversary of the contract, on the terms agreed by the parties. If the lease says nothing, there is no update. If the parties agreed to update it without naming an index, the rent is updated by the annual change in the IRAV.
And, in any case, the increase cannot exceed the result of applying the IRAV. Even if the lease says «CPI», the rise of a residential rent is capped by the IRAV. The index used is the latest one published on the lease update date: if the anniversary falls on 1 November, it will normally be the September figure, because October's will not be out yet.