If you use the majority of the A57 to Lincoln and want to avoid the A57/A46 roundabout you could go this route which takes you back on to cycle route 64 literally under the bypass. It's a great alternative to the roundabout particuarly at busy times.
https://ridewithgps.com/routes/33311872The Water Railway to the east of Lincoln has been closed this week between Lincoln and Washingborough due to the dismantling of one of the temporary bridges that have been put in place for the Eastern Bypass Works.
You can use the B1190 out of Lincoln still - it has been closed for months again for the Eastern Bypass works to vehicular traffic but they have put a temporary path in for cyclists and pedestrians.
You could then rejoin the Water Railway route at Washingborough.
Anyone planning to use the Water Railway east out of Lincoln once this weeks closure is over may find this site useful, as mentioned above the path can get flooded - there is a 50m section of it that is particuarly prone to flooding as they have lowered the path for the works.
The CCTV picture (updates about once a day) shows the path at it's lowest point - If it's not flooded here then you can be certain that it's not flooded anywhere else.
http://www.leb-sustrans-diversion.co.uk/Apart from the temporary closure the Water Railway is a good route and perfectly OK on a road bike.