Oh dear, this is not good. It's a great pity that you didn't treat the ground elder last year, but never mind. You really, really need to eliminate the ground elder before even thinking of laying turf, which I'm afraid means it'll be some time (possibly autumn) before you can lay any grass down. Ground elder is persistent and pernicious, and the only way I've found to get rid of it is to spray with glyphosphate (when its actively growing, the temperature's above 55deg F, and the soil is moist, but no rain is forecast). Then you wait 2 weeks. If its had no effect on the growth, spray or water it on again. Wait another two weeks. Now dig, removing every fragment of tiny root you can find. Now wait a month or so (if in May/June, six weeks if later), see what regrows. If it reappears, you have to go through the whole process again. Only when there's been no regrowth for 2 months minimum is it safe to lay your lawn.
Warning - the roots break easily, and the tiniest piece of root will grow, and if you lay your lawn over the top while its still there, you will end up with a lawn of ground elder within a year.