A lipping is an edge to man made timbers, i.e it covers the veneers on plywood for example. It can either be flush or have an upstand to prevent items falling off.
In this case you'll need a batten to hold the shelf up, on the left wall maybe but the other edge could be supported by either a batten on the side of the cupboard or maybe screwed through the cupboard sides directly into the shelf timber.
John
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