I believe you will have to either build a model for this or write some python code.
We had a vaguely similar situation where we had valves touching two pipes with some valves missing InstallationYear.
We wanted to look at the install years from each pipe and using some logic, clean up the missing data in the Valves feature class.
The way I approached this was to first find a geoprocessing tool that let me extract out a dataset of the valves and the pipe segments they touched. In your case, I think you could just pick out all lines that were touching? Then make sure the data was arranged in a proper order if it wasn't already.
Then loop through that data, doing the comparisons and calculations. This was trickier logic than it might seem because we sometimes touched two pipes, sometimes three and sometimes only one or even none.
(Also, we were going into an Enterprise GeoDB (Oracle) and were using versioned editing which creates another set of issues when it comes to scripting.)
But the starting point was to figure out how to get the data of interest cut out. I started this by hand in ArcMap and put the data into a file.gdb so I could look at the results. Once I had a technique that worked, I built a small model via Model Builder for getting the data. Then I pushed the model into Python and I now had a skeleton for working with the data I wanted. In my case, I could sort my data on a common field (the valve each pipe was touching.) I'm not sure how you will accomplish that except that maybe the data will just fall out in the order you want by definition of the line segments touching.
Hope this makes some sense and maybe points you in the right direction.
You might be able to accomplish this with Model Builder?
I'm just much more proficient in Python than MB and I had a number of conditions to work around so I needed the flexibility of coding.
FYI, by doing this in steps to file.gdbs, I could look at the data along each step. Once I knew things were what I wanted, I shifted to IN_MEMORY for the workspace of the file.gdb This allows for some fast processing times, assuming you have sufficient RAM.
Unfortunately, Data Reviewer is just that, only a review tool. It's great for finding issues but then the work begins.
Best of luck!