is Batman aware that they're coming?
how much history do they have, has the JL just formed or has it been going on for years?
possible outcomes>he isn't aware and JL just started
he'd survive an hour since he'd probably already have kryptonite on hand to deal with Superman, Green Lantern would probably get knocked out too, the rest would probably overwhelm him>he is aware and the JL just started
he's probably got a lead lined vault prepped somewhere for him to hide in and plan his counter attack
if Superman doesn't care about collateral he could literally crack the planet open like an egg and find Batman within an hour maybe two, if the JL just want to kill Batman but haven't gone psycho evil then it'd probably take a few days to find him
with so little time with the league, Batman would still be overwhelmed>he isn't aware but the League's been around for years
Batman would have indepth knowledge of the League but they'd have knowledge about how he operates too
Flash and Superman would go in first since they're fastest but would also most likely be taken out of commission quick enough for Batman to start preparing defences
MM would probably be able to disable most of the defences by phasing through them and WW would keep Batman on his toes in combat
in the end this is a coin flip victory>He's aware they're coming and the Leagues been going for years
Batman would have more than enough time to prepp the Cave's defences as well as whatever he'd need to incapacitate the League, their bloodthirst would probably throw him off and give them a slight advantage at the start, but Batman would adapt and incapacitate them
tl;dr Batman's greatest power is time