Unless you have spent years methodically removing all plants from your lawn except grass, then you will be amazed at what happens if you let sections of it grow to its natural full height. This need not look untidy; just a different form of lawn. We have a section of our garden where we have decided to let it grow long for the last two years - particularly in June and July when other flowers might be lacking. We cut round the edges so that the grass does not get into the borders and then my husband 'sculpts' paths through it so we can still get to the shed and compost heap without getting our legs wet.
You could be quite artistic with the mower and make squares or some other pleasing shapes so that is still feels like a garden rather than a weed patch.
Anyway the point is, we found to our delight that we now have quite a lot of bee-friendly extra flowers: several types of clover, common daisies (of course), self-heal, a small geranium and even some oxeye daisy.