Yes, that's right, they did both play in the 2017 team, although Laura was playing doubles with Joss Rae (and were actually a pretty decent team).Jo and Laura played on the same Fed Cup team more recently than 2013. They were part of the 2017 qualifying team under Anne Keothavong. I think Laura played doubles with her friend Katie Boulter.
This is them after beating Croatia and making it through to the playoffs..
I also remember Laura, along with everyone else being very supportive over the whole Nastase debarcle during the playoff with Romania. So they do have quite a bit of history. But maybe things have gone cold more recently.