Oh dear - I'm sorry to say the short answer is no. The usual treatment for bindweed is to insert canes where you see it growing, let it grow up the canes, then spray with glyphosate, repeating the treatments as often as necessary. Not really possible in a lawn, although if you don't mind your lawn being covered in sticks, you could do it, but you'd need to cover the grass when spraying with glyphosate or it'll kill that too.

Regular mowing should at least radically discourage it as if it can't photosynthesise it will be in trouble. I'm just wondering too whether a lawn weed killer would have some effect -you would have to let it grow a couple of leaves and then leave it for the specified period. Its a long shot as the blessed stuff is so deep rooted. Have you got the one with large white flowers or the much smaller pink flowered field bindweed which might respond better to that?

If you slide a large bottomless and topless milk carton over the cane that you've allowed the bindweed to grow up, then take out the cane, allowing the bindweed to collapse inside the carton, you can then spray within the carton and protect the grass. Even more unsightly than sticks all over the lawn though!