Binary Search Algorithm in JavaScript
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 &lt;= 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)]
    &amp;&amp;
        searchedValue !== list[++i]
    ) {
        if (--tries &lt;= 0) {
            return ("NOT FOUND");
        }
        if (searchedValue &gt; list[i]) {
            lowerBound = i;
        } else {
            upperBound = i;
        }
    }
    return i;
}