I'd lift the turf and either stack it to let it rot down or put to one side and as you start to dig the new border bury it a spade depth down grass side down. That way it adds humus to the soil and an instant fertiliser.
Rodge, How much lawn and would you hire a rotivator? If it is a lot of lawn you can hire a lawn lifter which will slice the top off the lawn which you stack in a corner somewhere grass side down is the way I always did it, it gave me wonderful loam for seed trays a year later. It can be dug in by digging a trench and laying the turf in the base then covering with top soil this is hard work depending on how much grass you are taking up. You could just double dig it in making sure the grass is facing down after all farmers plough it in, problem would be dormant weeds, you would need to keep on top of those for a couple of years.
Good luck with your border, any new feature will initially be hard work but then you sit back and enjoy your labours.
If it's only 30x10 you can do that in half a day to lift and another day or two to dig. Depends how fit you are and the money you have to waste. I'm tight fisted by the way.