Assume I have a program like baker payouts or an arbitrage bot that I am running on my computer and I want to sign it automatically the operations with a private key that I have on my ledger depending on conditions met in my program. Is this possible? From my experience the ledger always requests me to push the physical button to sign any operation I perform on Tezos. Obviously this is for security, but is there anyway around this? Any there any libraries that are used for signing with a ledger?
No, there is no way to bypass the requirement to ack a transaction. You would have to write your own ledger-tezos app to support this. It can be done, as the baking app signs blocks without interaction using the same key. You would have to code a new instruction to sign without user button.