Typerbole says that about 0.1% of onchain txs are LN open/closes.
Currently, we have about 7.5M txs/month.
That's about 7500 LN onchain txs/month.
Those 7500 LN onchain txs account for, conservatively, 750k txs/month on LN. 
LN scales  by at least a factor 100.