I think I'd do what Sharley said : "to save others from the plights suffered by L and R."
Apart from anything else there are too many s/z sounds squashed together in Lizzie and Robyn's plights - sounds like "splights" , though that might just be me. Feel free to ignore!
Thank you both. I think, actually, I will leave as is unless someone tells me it's wrong, because although I agree, Jem, that it isn't hugely elegant as is, it isn't hugely elegant the other way either...
It's in my covering letter, so hope it isn't a turn-off.
The second one is grammatically correct, but lots of people would say the first and believe it to be the grammatically correct version. I, too, would avoid that particular construct, and rephrase as has been suggested.
If they're sharing the same plight, it's acceptable to use just one apostrophe, on the second name. Here, however, you have 'plights' (plural) so you would need apostrophes on both names, because their plights could be different.
It would be liking saying, 'to save others from Lizzie's anger and Robyn's manipulations' because they're two different things, or, if they're both manipulators, 'to save others from Lizzie and Robyn's manipulations'.
Ah, Terry, many thanks for the full explanation. That makes perfect sense. Fortunately I had already changed it so both names had apostrophes before sending off.