If your hen needs calcium you shouldn't need to trick her to eat egg shells, she should just go for them. They don't look appetizing to us, but to a hen short of calcium they look delicious. We wash them lightly to break the inner lining and just let them sit to dry then crush them to pieces about 1/4 inch in diameter. Over the years the pure bred chickens we have purchased have seldom lasted more than four years. Our cross breeds have lasted much longer, but not a whole lot made it over a decade. Don't feel you have failed if this one doesn't make it. Some just don't and its really hard sometimes to pinpoint what is wrong.
Romaine is better than iceberg lettuce but only barely. Kale, collards, turnip greens are better and kale is supposed to have lots of calcium. Chickens need greens and much more than people think, but grass will do as do many weeds without paying money at the grocery store. I feed my chickens an array of greens from the garden and the yard. Here is one article.... plenty more out there.
http://www.fresheggsdaily.com/2012/02/winter-weeds-101.html I have been learning weed identification over the years to be sure which are safe. That is fun and educational as well. Greens make the yolks much deeper color and I trust my chickens to eat what they need and leave the rest. Mostly they want more.
Old dogs can learn new tricks and so I am starting to experiment with fermenting feed which I just heard about here on BYC and have been researching. You can sprout grains as well. Seems like more trouble tho....Being in the south I just plant wheat in the winter garden and harvest it with scissors...that that the doves miss.