Even with a slower transaction speed than Visa or MasterCard, Litecoin can offer something that they cannot: availability. With accounts being frozen in Canada and sanctions being applied to Russia, those that did not prepare in advance for that are likely feeling the pain now.
Litecoin competes with the regular payment systems in another way. It provides a freedom that they do not provide, and it also provides protection from inflation (if you don’t jump in when the market is hot and the prices are unreasonably high). The disinflationary rate of Litecoin will continue to decrease until it disappears entirely (unlike most fiat currencies out there, which there is no upper limit on the supply of the currency).