For the Lavender Town thing, go to Celadon City and in the Game Corner(or something similar) press the A button on the poster. You will then battle a Rocket grunt. After a stair will appear and lead to the Rocket Hideout. Go into it and find Giovanni, after beating him he'll drop a Silph Scope. Pick it up and go back into the Ghost Tower. Then you'll be able to continue.
I hope I helped.