  In the paper, we extend the ADC property to the representation of quadratic
lattices by quadratic lattices, which we define as $ n $-ADC-ness. We explore
the relationship between $ n$-ADC-ness, $ n $-regularity and $ n $-universality
for integral quadratic lattices. Also, for $ n\ge 2 $, we give necessary and
sufficient conditions for an integral quadratic lattice with rank $ n+1 $ or $
n+2 $ over local fields to be $ n $-ADC. Moreover, we show that over any
totally real number field $ F $, a positive definite integral $ \mathcal{O}_{F}
$-lattice with rank $ n+1 $ is $n$-ADC if and only if it is
$\mathcal{O}_{F}$-maximal of class number one.
