  In this paper, we introduce an element $\phi$-$\delta$-primary to another
element in a compactly generated multiplicative lattice $L$ and obtain its
characterizations. We prove many of its properties and investigate the
relations between these structures. By a counter example, it is shown that if
an element $b\in L$ is $\phi$-$\delta$-primary to a proper element $p\in L$
then $b$ need not be $\delta$-primary to $p$ and found conditions under which
an element $b\in L$ is $\delta$-primary to a proper element $p\in L$ if $b$ is
$\phi$-$\delta$-primary to $p$.
