How reliable is sewer re-lining?
Yes it is reliable and very common with municipalities to extend the life of their sewers and water mains.  

The only downside is that the inner diameter is reduced.  Also they do still need to dig at least two holes to install the liners.

When I had this quoted, the opposite was true - digging up the sewer was cheaper than a liner, so make sure to get a few quotes from reputable contractors.