What doesn't work properly

As pointed by @Roland Illig's answer, your solution produces an error when list contains only 1 item and this item doesn't match el.

It comes from the fact that:

• for a 1-item list, LIM is 0
• after the while() expression didn't find a match, --LIM gives -1, which evaluates to true
• so if (!--LIM) is false and the loop continues infinitely...

This issue can be solved by merely changing this test to if (--LIM <= 0)

Possible improvements

As pointed by @Dair, your names are some cryptic.
For the sake of readability you'd better to change:

• el to searchedValue
• LIM to tries (also note that using uppercase is supposed to be reserved for constants, while this data is not)
• lb to lowerBound
• ub to upperBound

Also, following best practices, I recommend to use block marks for if()s.

All that said, here is a suggested improved (and corrected) version:

function search(searchedValue, list) {
    var tries = Math.ceil(Math.log2(list.length)),
        lowerBound = 0,
        upperBound = list.length - 1,
        i;
    while (
        searchedValue !== list[i = ~~((lowerBound + upperBound) / 2)]
    &&
        searchedValue !== list[++i]
    ) {
        if (--tries <= 0) {
            return ("NOT FOUND");
        }
        if (searchedValue > list[i]) {
            lowerBound = i;
        } else {
            upperBound = i;
        }
    }
    return i;
}

What doesn't work properly

As pointed by @Roland Illig's answer, your solution produces an error when list contains only 1 item and this item doesn't match el.

It comes from the fact that:

• for a 1-item list, LIM is 0
• after the while() expression didn't find a match, --LIM gives -1, which evaluates to true
• so if (!--LIM) is false and the loop continues infinitely...

This issue can be solved by merely changing this test to if (--LIM <= 0)

Possible improvements

As pointed by @Dair, your names are somewhat cryptic.
For the sake of readability you'd better to change:

• el to searchedValue
• LIM to tries (also note that using uppercase is supposed to be reserved for constants, while this data is not)
• lb to lowerBound
• ub to upperBound

Also, following best practices, I recommend to use block marks for if()s.

All that said, here is a suggested improved (and corrected) version:

function search(searchedValue, list) {
    var tries = Math.ceil(Math.log2(list.length)),
        lowerBound = 0,
        upperBound = list.length - 1,
        i;
    while (
        searchedValue !== list[i = ~~((lowerBound + upperBound) / 2)]
    &&
        searchedValue !== list[++i]
    ) {
        if (--tries <= 0) {
            return ("NOT FOUND");
        }
        if (searchedValue > list[i]) {
            lowerBound = i;
        } else {
            upperBound = i;
        }
    }
    return i;
}