If you seed new grass seed now, you will sprout the new weeds along with the grass. What I would do is start immediately sprinkling the entire lawn area 3x per day for just a few minutes. Do that for 7 days and you'll sprout more weed seeds. Then spray those new weeds with Round Up and seed the next day.

Where do you live? It's getting late in the season to start this project. Most people should have started this 6-8 weeks ago.

Live in NC, seeded last year on Halloween after spraying with roundup 3 days earlier and had a great looking lawn until the heat and drought killed it off this June/July. Didn't have any problems with weeds sprouting with grass last fall, just wasn't sure if using a different herbicide this year would have an unintended pre-emergent effect. Can't imagine starting a lawn 6-8 weeks ago, we've had drought and temps in the 90's until this week.