TYPO3 Core

1. Setup the following TypoScript:

lib.parseFunc_RTE.nonTypoTagStdWrap.HTMLparser.tags.ul.fixAttrib.class {
    default = myownclass
    always = 1
}

2. Add the following content inside a RTE

<p><a href="t3://page?uid=1">Link number one</a></p>

<ul>
    <li><a href="t3://page?uid=1">Link insude a list</a></li>
</ul>

3. Watch the results in Frontend

Expected behaviour:
The first AND the second link have an additional class "myownclass"

<p><a href="/" class="myownclass">Link number one</a></p><ul><li><a href="/" class="myownclass">Link insude a list</a></li></ul>

Actual hevaviour:
Only the first link has the additional class "myownclass"

<p><a href="/" class="myownclass">Link number one</a></p><ul><li><a href="/">Link insude a list</a></li></ul>

Version: TYPO3 9.5.22