The most common problems i have observed in LN are
2. Limitation of funds transfer through channels, unfortunately LN will not support big/bulky transactions, you have to rely on your active channels and their capacity.
That's ok because the "vision" for the Lightning Network is to accomodate your day to day
micro-transactions, which is not practical to do on-chain, with "unfairly" cheap fees.
But if you want to send $1,000,000 of Bitcoin, then doing it on-chain should be the only way in my opinion.