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We determine the quantum filtration structure of the Lee homology of alltorus links. In particular, this determines the $s$-invariant of a torus linkequipped with any orientation. In the special case $T(n,n)$, our resultconfirms a conjecture of Pardon, as well as a conjecture ofManolescu-Marengon-Sarkar-Willis which establishes an adjunction-typeinequality of the $s$-invariant for cobordisms in $k\overline{\mathbb{CP}^2}$.We also give a few applications of this adjunction inequality.

Lee filtration structure of torus links