how can i get rid of ground ellder it is growing in my clump of day lillies without digging up the whole patch.

That's a difficult job - you could try shielding the Day Lilies and then treading the ground elder down to bruise it as much as possible, then water weedkiller very carefully on the ground elder - still shielding the Hemerocallis maybe with plastic sheeting?
The weed killer need glyphosate in it. You'll probably have to repeat this several times. The only other way is to dig up the precious plants and then deal with the elder. It's not easy to get rid of. Sorry!

You could use a contact weedkiller like Roundup, Hollygate. But don't spray it on or you will also hit surrounding plants. Make up some of the weedkiller in a bowl, put on a plastic glove and dip your fingers into the solution. Then fondle the leaves of the ground elder without touching other plants. This works well for me.

i think ground elder is indestructable , the plot of land next to ours is riddled with it , and the owners have used all sorts on it and it's still there.it has got a hold in our herbacious border and all we do is pull off every leave we find in an attempt to starve the plant of energy. this has worked to a point but you need to be out every day to do this.................steve

To add to Bulbaholic's answer, if you add a drop of washing up liquid to the weedkiller it clings onto the foliage better when you do the fondling. (love the thought of that, I'd rather strangle it!)