[Everything] Do the Lannisters have a fighting chance?

In response to the OP, no. Unless Euron Greyjoy can whip up a hurricane and decimate Daenerys's fleet, or a Kraken frightens off the Dothraki halfway to Westeros, I fail to see how the Lannisters can beat Daenerys in battle. However in terms of whether there will be at least one Lannister left standing who is able to inherit Casterly Rock, then yes, there is a good chance of that happening.

Tyrion is very strongly in Daenerys's favour right now, so as long as he doesn't get himself killed in a battle/assassinated, he'll be fine. Because Daenerys's Essosi army is so massive, Tyrion is probably the most likely candidate to receive the Lannister inheritance. That said, his wellbeing has largely depended on how successful Daenerys has been so if Daenerys falls, he almost certainly will do too.

I don't believe Cersei has a chance at all. Due to the chaotic politics of Tommen's reign, only the Crownlands, Westerlands and Stormlands are still under the control of the Iron Throne. That's simply not enough to combat Daenerys's force. It'll only be a matter of time before she snuffs it one way or another. I wouldn't include the Riverlands here as it was Jaime who personally pressured Edmure Tully into working for him, so I think whatever decisions Jaime makes will over-ride orders from KL.

As for Jaime himself, he has shown many a time that it is possible for him to think and act independently, but whether he lives or dies will depend on whether he chooses to stick with Cersei or not. If he does, it will be the death of him. Assuming that Daenerys is successful, Jaime (if he survives up to this point) will need to overcome any grudges against Tyrion for killing Tywin and reconnect with him, as Tyrion will be his most crucial lifeline if and when he ever faces Daenerys. There are many hoops for Jaime to jump through to ensure his survival but assuming he makes the necessary calculated decisions on time, his survival won't be impossible.

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