If spring and fall are your only choices I'd pick spring as the number of hours of daylight are longer in the spring than the fall.
Not sure why you'd want to spent 5 nights in Lucerne, while the city is pituresque and worth visitng I would suggest to spend a day or two in Lucern and than the rest of the time in the Bernese Oberland area, which is a short train ride from Lucerne.