You should be able to use the translate function to convert your umlauts to standard characters. So you can just update your example to the below:
<xsl:value-of select="translate(@lastname,'ä','a')"/>
I used the character encoding of that character in the translate because my process was giving an error about the specific character encoding but either should work.
Also, if you have additional characters you would just add them to the translate function as well.