We have only booked when we arrive, but if you are visiting over the weekend and your plans are fairly fixed then booking before hand will give you piece of mind
It shouldn't be too busy in June unless you're going during half term or during the weekend ?
so you should be able to book when you arrive.
For peace of mind I phoned DLRP restaurant reservations, before we went, it was very quick and simple.
When we got there we wanted to change a few things (day for Auberge de Cendrillon) the hotel consierge did that for me and (time at the Blue Lagoon) I did that myself at the restaurant.
If you change your mind when you get there you can always, change or cancel the reservation.
I would definitely book in advance if it falls on a Friday, Sat or Sun. Otherwise you should be fine to book on your day of arrival at the hotel. Have fun!