It's tarmac to Bardney, then gravel or take the short road alternative to Southrey. Then Tarmac to Martin Dales. The water railway becomes gravel beyond into Boston. A few gates here and there but not too many. From there take the road the other side of the Martindales bridge to Dogdyke rejoining the official route. I plan to take a lanes route from Kirton Lindsay to Bardney then Southrey as above. It's a gently descending route down to Bardney and avoids the choppiness around Lincoln. Means you miss food opportunities in Lincoln so you'd need to stock up at Glews garage, Goole. Did most of that in reverse during our Easter Arrow, this year, when we controlled at Woodhall Spa. The lanes are quiet and well away from those Eastern bypass works. No extra distance over the official route.
PM if you'd like a copy of my alternate southbound GPX track for that leg, plotted with my recumbent in mind. If you want to go via Lincoln then my only comments as above jump on road Bardney to Southrey rejoin water railway then road from Martindales.