Hiya dev,
The 'style' part of the first example you gave is: style="width:50px;"
<li><span><a href="index.html" style="width:50px;">Home</a></span></li>
It should work fine if you place the inline style into the same relative format and position in the second example:
<li><a href="<?php echo($assumedRoot); ?>index.php" style="width:50px;>Home</a></li>
Inline styles supercede external stylesheets, so whatever styles you put in there should be effective.
The format is:
<someTag ID=TheElementID style="style-property:this_value; style-property:this_value;" /> What ever content you are putting between the tags </ClosingTag>