Talking of skip-diving, really heavy PVC lino is great (industrial stuff is best), easy to cut into 15cm widths and strong enough to stay straight upright if the bed behind it isn't more than say 3cm below the lawn. Obviously the more wibbly-wobbly the lawn edge is the stiffer the lino will be. You could try folding a wider strip of lighter gauge and fitting fold-upwards - a hot air gun would help for a neat job.
But it has to be fresh - not really old, so it isn't brittle and will stay like that for several years, and then come out in one piece when its edge finally starts to go.
High quality carpet tiles are a possibility.
Depending on your area's housing profile, quite big pieces of UPVC fascia cladding can turn up in skips, but only useful for straight lines (and far too valuable really - so good for raised beds).