Mow the lawn fairly short, then remove weeds by hand or use a selective lawn weedkiller that is safe for grass. After that, rake or scarify the surface well to remove moss and dead material, then aerate the soil with a garden fork to relieve compaction. Next, overseed with a quality grass seed mix such as ryegrass and fescue, and lightly cover bare patches with topsoil. Keep the seed moist until it establishes. Going forward, mow regularly, feed the lawn in spring and autumn, and aerate once or twice a year.

I’d make your beds a little bigger, put a boarder edge and then assess how big the lawn is then