According to the "Pokemon FireRed" walkthrough on IGN, the best way to get from Celadon City to Lavender Town is by cutting through Saffron City, which lies directly between the two locations. However, in the early stages of the game, Saffron City is inaccessible until the player gives the city's guards tea from Celadon City's condominiums.
IGN further explains that the only way to get to Celadon City without cutting through Saffron City is to take Route 8. Route 8 lies to the west of Lavender Town and has plenty of trainers to battle with along the way. At the end of Route 8 is a small building that resembles a house. This building is the entrance to the Underground Path, which leads directly to Celadon City.
Bulbapedia states that there is an old woman on the first floor of the Celadon condominiums who will give the player some tea. This tea will quench the thirst of Saffron City's guards, enabling the player to use the city as a shortcut to travel between Lavender Town and Celadon City. Passing through Saffron City is much faster than taking Route 8 and the Underground Path, especially since the player will not have to battle any trainers along the way.