When you compete with someone else , you are not locking that other person in place where they can not compete with you.

LN Locks BTC in Place ONCHAIN, once locked there can be no future transactions fees for the miners on that amount of BTC until LN releases the lock.
However LN can makes an infinite amount of transaction fees OFFCHAIN on that locked amount, while for the miners it is frozen.

Stealing is an accurate description of what LN will do to the miners.
They are stealing the ability of the miners to make transaction fees from the Locked BTC.

To get a Competition you need Litecoin or another Altcoins, because at no time , does one directly block the other from receiving transaction fees.
(They are competing against each other.)