The roads condition is pretty bad in Nepal. The roads are good only in the major cities, as soon as you go outside the cities, you will find only single lane broken roads. When you drive from Lucknow, the roads are smooth till the border after that the condition is below average. I went by bus to Nepal which was really a bumpy ride; and by my experience, your sedan car with 6.85 inches clearance will perform good. Don’t think twice, just drive to Nepal. You will have a wonderful experience. There will be parts when there are no roads, you will have to go really slow and manage at those times, rest all is good. Just Go!!
It would be better if you could manage to get into matadoors (tempo travelers) that run between the two places, it takes them around 6 hours while the busses take nearly 12-14 hours for the same distance.
The road is fine mostly but in between there's a patch which is risky due to frequent landslides.