Lighted and lit each work as the past tense and past participle of the verb light. Both have long histories in English and are used throughout the English-speaking world, so you are generally safe using the one that sounds best to you. Keep in mind, though, that lit is generally favored for both uses outside the U.S. (though lighted, again, appears some of the time). Lighted, where it does appear, is usually an adjective (e.g., a lighted grill), while lit is more often a verb (e.g., she lit the grill).
Neither form is inherently more American or more British. Both forms are hundreds of years old, and each has had periods of prevalence throughout its history. It just happens that at this stage in history lighted is more common in American English than elsewhere.
This ngram graphs the use of lighted and lit in American English from 1800 to 2019.
And this ngram graphs the words’ use in British English during the same period.
Of course, these Ngrams don’t show how the words are used, but they at least suggest that usage has been far from consistent.
The news lit up the Web like a brush fire. [USA Today]
Amid the greenery of the serene indoor bamboo pond were lighted balloons shaped like extraterrestrials. [New York Times]
When a circle of lit candles was placed on the cake it was supposed to glow like the moon. [Arizona Republic]
In September, a good portion of the Internet lighted up with the news that DMX … was somehow unfamiliar with Google. [LA Times]
Outside the U.S.
He suspected youngsters had lit plastic bags filled with gas. [New Zealand Herald]
Vancouver author Zsuzsi Gartner is a lit firecracker left unattended on a summer lawn chair. [Winnipeg Free Press]
The attackers lit tyres inside the mosque in Al-Mughayyir village. [Telegraph]