I've not tried thyme, but doubt that it is more dog resistant. My lawn looks quite green, mostly because of moss! Is it the dog urine that's making your grass die, or their playing & digging?

I'd be wary of either. If they flower, both are magnets for bees. Not a good combination with dogs.

Would you consider replacing your lawn with a 'hardcover' such as bark mulch, pebbles, pavers?

I have three dogs and very little lawn. They all enjoy snooting through the shrubs and sunbathing on whatever piece is warm at the time. However, they rarely play here. If your dogs are using the lawn to play on then a firmer surface may be better. Sharp. well-packed grit will help to keep their claws short and their pads tight - and it's easy to clean up, too.

Hi, it is one particular patch at the edge of the garden that they seem to favour, the rest is quite green.
The bare patch is right by the back door so as soon as we open the door they kind of bound straight onto it, which is why i thought perhaps using some kind of ground covering plant.