System.LimitException cannot catch by [try...catch...] in Apex.
When call Apex method in lwc and LimitException occurred in Apex source, [try...catch...] also not working in js.
But LimitException can be catched by [Promise.catch]
Sample
Promise.all([
promise1,
promise2,
promise3
]).then((values) => {
console.log(values);
}).catch((error) => {
// LimitException can be catched here
console.error(error);
}).finally(() => {
console.log('Experiment completed');
});