We prove some results on weakly $\delta$-primary elements and weakly 2-absorbing $\delta$-primary elements in a multiplicative lattice. A sufficient condition for a weakly $\delta$-primary element (weakly 2-absorbing $\delta$-primary element) to be a $\delta$-primary element (2-absorbing $\delta$-primary element) is proved. The concept of an expansion function of elements is introduced on a product of a finite number of lattices. Some results about weakly 2-absorbing $\delta$-primary elements in a product of lattices are proved.