how to find a td by index in jquery

As Sakil said you can use eq(). Try this:

function LFLS() {
    // load from local Storage
    for (i = 0; i < localStorage.length; i++) {
        key = localStorage.key(i);
        row = key.split(",")[0];
        col = key.split(",")[1];
        // how to get the cell by row and col
        $("table tr").eq(row).children().eq(col).html('NEW VALUE')
    }
}

I believe you need the following snippets.

Before your for loop

const rows = $("table tr");

After you obtain row & col variables

const cellToUpdate = rows[row].children[col];

Alternatively, if you're looking to programatically loop through the table you could use the following snippet.

<script type="text/javascript">

    const rows = $("table tr");
    for( i = 0; i < rows.length; i++ ) {
        const currRow = rows[i];
        const rowChildren = currRow.children;
        for( n = 0; n < rowChildren.length; n++ ) {
            const cell = rowChildren[n];
            cell.innerHTML = "My new data for row: " + i + " in cell " + n;
        }
    }
</script>

Is something on the lines of below not going to work for you for some reason?

$("table tr:nth-of-type([your-row])).eq([your-col]).html([your_content]);