Spurs fan coming in peace. I've got a lot of love for European football so have huge sympathies for Palace potentially not getting the rewards their season deserves.
I imagine the appeal will largely revolve around Textor's involvement but I think Palace should at least try and make the argument on another front too.
There is precedent that the FA Cup in England has been considered more worthy than league placing in the past.
Wigan's FA Cup win forced 5th placed Tottenham in to a qualifying round because Wigan were ranked higher:
2013–14 UEFA Europa League - Wikipedia
I'm pretty sure there have been other examples where scheduling conflicts have given favourability to the FA Cup winners over English clubs league position.
Really, Palace should be arguing that they've qualified as England's sixth best club which is equal to Lyon. Their 12th place finish isn't the criteria they've qualified on so shouldn't be relevant.
I don't know how UEFA would resolve two clubs that are both equivalent to 6th but surely in this football world that favours the elite there's an argument that the higher ranked league should take priority.
If both can't qualify I'd really be pushing for Lyon's removal because Palace are theoretically ranked higher than 6th place Villa and unless the rules have since changed, there's precedent for it with Wigan.