In reply to The New NickB:
Neither were solo. Neither were 'unsupported'.
Hargreaves benefited greatly from a beaten path, the route made, and the psychological benefit of other climbers around, fixed ropes to descend if necessary etc. This is not comparable to Messner's 1980 true solo - no people, no ropes, no camps, no track, no help.
Lydia was officially on the South Pillar route with Ball and Hall but when it became obvious they would not climb that route she joined with other climbers and 'illegally' did the South Col route. She was only climbing alone for the upper ridge section.
There was confusion, with serious consequences, over the Spanish reports of her condition. It was initially reported that she was exhausted, crawling, in a bad way, and thus unlikely to have been able to make the summit. It later transpired that this was a miscommunication and the Spanish did not think that at all, and they believed she went to the top - partly because she described things there one could only know if you'd been there.