For example, there is a limit of 2M sats per transaction when sending sats from Phoenix LN address to onchain address. I believe that transactions between LN addresses are not limited (other than by the overal capacity of your channels), however, the reliability of lightning payments exceeding 3M sats goes drastically down, as confirned also by Juraj Bednar https://www.google.com/amp/s/juraj.bednar.io/en/blog-en/2022/10/27/test-of-bitcoin-lightning-wallets/amp/