I use a big 'tupperware' cake box to store the lids and then store the boxes inside one another. I keep them on a swing out shelf in a corner cupboard.
Lakeland sell boxes with matching coloured lids. They are brilliant and I will only buy those in future.
Sadly, I still have all the usual old stuff. I did once pair all the lids and boxes and throw away all the ones that didn't have partners. What I had forgotten was all the boxes used to store various things all over the place in boxes without their lids (vitamins in the kitchen cupboard, perishable flavourings in the fridge, lego on the toy shelves) which will, now, forever remain lidless. Hey ho.