The method you describe sounds like it's taken from other models, as the Laguna II speedo is an electromechanical gauge, and not a digital display.
The speedo here can't flash, but holding the trip computer button while inserting the keycard invokes the self test mode. (I know the Espace III and IV and the Scenic II differ here.)
Nevertheless, I tried the method you posted, and despite me keeping both the trip computer button (unlike Scenic and Espace, the Laguna has only one) and the starter button depressed for at least ten seconds,
the only results were that the speedo went into self test mode, and the engine started.
Yes, I did keep both buttons depressed after the engine started.
Looking at a similar thread on Espace (Renault Espace - Interiors - Switching Espace Speedo from km/h -> mph
), it's said there that the method differs depending on whether the car is equipped with keyless entry or not.
I'm not sure whether this aspect has an impact in the case of Laguna or not, though.