Ten years ago, we produced our guide called Canoe and Kayak Journeys of Lanark County.
Many things about our landscape have changed since then. For example on Route #1 Beckwith Township; Glen Isle on the Mississippi mentions there are several picnic spots towards Carleton Place. All of the land in this section is now privately owned and picnics are not allowed unless by permission of the owners. You will have to eat lunch from your vessel or back at your vehicle.
Several other journeys listed in the guide suggest lunch spots on deserted islands. Watch for and respect private posting signs on all private property.