I live just east of Lincoln. The route you plan to approach Lincoln from the west is one that I would like to do one day. I think it is also known as the Dukeries trail. One of its landmarks is Fledborough viaduct
http://www.forgottenrelics.co.uk/bridges/gallery/fledborough.html
I would stay on route 64 myself which takes you all the way in to the centre of Lincoln and then follow the Water Railway path out to Bardney (National cycle route 1). As others have indicated it is entirely suitable for 700x28 road tyres
http://www.sustrans.org.uk/assets/files/leaflets/Harby-Lincoln.pdf
To get on the sustrans path to the east of Lincoln you might find this useful
http://goo.gl/maps/oy7pB
Theres a 50m stretch near Foss street which is supposedly not part of the cycle route and is a designated footpath only, I ignore this and stay next to the the Foss bank. The route takes you along side Brayford Pool and under the A57 Wigford Way. It would be easy if you could stay next to the river but this will make it awkward
http://www.narrowboatworld.com/index.php/gallery?func=detail&id=62
Following the google map will mean that you will have to walk about 100m in the town centre. Ignore the wild detour google sends you up and down the A15 just use the pedestrian crossing ! You could stay on the roads if you prefer though.
Theres nothing particuarly worrying about your route through Lincoln but I note you're planning to do this on a week day. The roundabout on the A46/Skellingthorpe Road and B1190 out of Lincoln are to me less preferable than the alternative, especially if you happen to be along here at rush hour.
Further east I would skirt round the south of Horncastle but then take a slightly shorter route to Spilsby. This route follows part of a local Audax event route.
http://goo.gl/maps/zKXE4
If you fancy a short detour to Hagworthingham to vist the almost legendary JJs cafe then turn left at Lusby. Its visited often on Audax events and local club runs. You'll be hard pressed to find a piece of cake (big) and a cup of tea for the same price anywhere.
You could visit Woodhall Spa on the way back if you fancy varying the route a bit. Its a rather nice largish village with a range of shops/cafes etc.
http://www.woodhallspa.org/index.html
http://www.woodhallspa.org/leisure_waterrailway.html
Theres a photo on the above link that shows the unsurfaced 'summer' part of the route near Bardney with the sugar beet factory in the distance
The route back to Bardney on the road is fine but using the sustrans path is shorter.