Torah Temimah cites Toras Kohanim (Sifra, Vayikra Dibbura DeChovah, Section 10).
Sefaria — Toras Kohanim (Sifra, Vayikra Dibbura DeChovah, Section 10)
“And he shall bring his asham to Hashem” — for the sake of Hashem (lishmah).
Diyuk of “la-Hashem” — requirement of lishmah for the asham / oleh ve-yored.
The middle-tier offering of the oleh ve-yored must be brought with intent for the sake of Hashem. Improper intent (she-lo lishmah) can invalidate the service. The Sifra’s reading of “to Hashem” establishes that this requirement applies even to the sliding-scale chatas that is sometimes termed asham in the verse.