Как заменить все входящие элементы внутри одного блока?

Если именно регулярками, то можно так:

$str =<<<STR
    <ul class="test-2-ul-class">
        <li class="test-li-class">
            <p class="other-class">Text1</p>
            <img class="replace-text" src="/img1.png">
        </li>
        <li class="test-li-class">
            <p class="other-class">Text2</p>
            <img class="replace-text" src="/img2.png">
        </li>
        <li class="test-li-class">
            <p class="other-class">Text3</p>
            <img class="replace-text" src="/img3.png">
        </li>
    </ul>

    <ul class="test-ul-class">
        <li class="test-li-class">
            <p class="other-class">Text1</p>
            <img class="replace-text" src="/img1.png">
        </li>
        <li class="test-li-class">
            <p class="other-class">Text2</p>
            <img class="replace-text" src="/img2.png">
        </li>
        <li class="test-li-class">
            <p class="other-class">Text3</p>
            <img class="replace-text" src="/img3.png">
        </li>
    </ul>
STR;

$str = preg_replace_callback(
    '~<ul class="test-ul-class">.+?</ul>~s',
    function($m){
        return preg_replace('~<img class="\K[^"]+~', '***', $m[0]);
    },
    $str
);

print_r($str);