New growth tastes delicious. Have you ever tried it? It's tender and sweet, and few animals can resist it - even birds, squirrels and rodents will steal fresh blades.
I would reinforce the command "leave it" from a distance beginning with no distractions and slowly increasing the difficulty. This allows you to stop the behaviour from a distance.
Secondly I would add the following to their diets during this time of year - a green food supplement (easy to find at a health food store or even some grocery chains) made of green "superfoods". There's LOTS to choose from.
Last, purchase a few flat trays, add some organic soil and some organic oat seed. Grow them their very own grazing station, they will love it. When the tray is almost ready for new grass, I spray a few spritzes of lite salad dressing on them... lol... I know, silly, but they really like the oil and the sundried tomato. Spoiled? Nah...
But "leave it" is what's ultimately going to solve the problem - the other suggestions simply reduce the drive to eat the lawn and make reinforcing "leave it" a bit easier.
Good luck, it's not an easy habit to break, but consistency is key, as with anything.
My favourite solution is to replace the lawn with natural (uncoloured) cedar chips. This gives you a very porous product that is easy enough to dispose of and makes for easy cleanup when dealing with loose stools. Few dogs show any interest in eating cedar (tastes horrible) and the smell is lovely - and keeps away bugs like mosquitoes, fleas, ants and ticks.
Every spring we get a new shipment to keep the yard fresh.