Heather playing too conservatively and Lee has upped her game, now one set all and really not good enough from Heather who should not be making such a drama of beating a player ranked 240 in the world. Given her draw there are no excuses for not making the QF here.
Heather wins and that's really the only positive to take from her performance. I'm not sure this will do much for her confidence, struggling to beat a player outside of the top 200 hardly promises great things to come. Overall since Wimbledon her form has been poor and she seems to be struggling a lot with her game. Maybe she might be forced to play a bit more attacking in her QF but certainly today she just kept waiting for errors from Lee which came in the first set but Lee upped her game in the second. Its her first WTA QF for quite a while so I'm sure she's relieved but she can't be under any illusions that shes had a plum draw and struggled to beat two players who really should not be giving her so many problems.
She always seems to start tournaments scratchily and improve during them, which is why this is probably a good standard tournament for her when she can scrape through without playing very well. Useful points too, and a win in the Quarter-Final would likely put her back in the top 50.