This issue is seen quite often with areas where hard surfaces meet lawns, especially corners. I see this where I live, and just feel a shrub or something similar will suit better. If you want to keep the lawn there, I'm afraid it will mean yearly top dressing of sieved top-soil and spiking in spring or autumn, and in the summer months you will find you may need to water it more often. Most likely due to lack of soil or obstructions around the edges.
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I live in west central Scotland - not where that photo is...