What are your intentions for the ex lawn Jennifer? If you want to garden it I'd slice the turf off and dig it over. Turf can be composted and replaced in time. Weed surpressing membrane is more about stopping weeds coming up through gravel, bark etc than killing them. As Goldilocks says, they're not light proof.
The slice off and dig method has the advantage of now rather than waiting. Anything like twitch or other persistant weeds would still be lurking when the grass had gone and you could be getting on with eliminating it. It's not difficult in an empty bed, it's when it's round all your precious plants that it becomes impossible.