Answer
You do not need to buy a ticket to enter the Palacio Legislativo: you can enter the building without purchasing a separate admission ticket. This makes the palace a convenient stop on a Montevideo itinerary, even during a short visit.
Photography is allowed inside, so the building is not only interesting from the outside. The interiors, with their marble, bronze, wood, halls, and staircases, reveal how Uruguay envisioned state authority and the stability of the young republic.
The palace remains an active government building, not an ordinary museum. Visits depend on opening hours, entry screening, and accessible areas, so allow time for formalities and behave as you would in an official institution, even if admission is free.