In this article, we develop the technique of disjoint elements in order to describe the order bounded set in the \(L_p\) -spaces. Based on this, we introduce the notion of \(L_p\) -order bounded in general Banach lattices and establish some corresponding characterizations. As applications, we characterize lower p-estimate Banach lattices and upper p-estimate Banach lattices in terms of weakly p-summable disjoint sequences. Furthermore, we introduce and investigate two types of operators related to \(L_p\) -order boundedness. The relationships between two new types of operators and classical notions of operators, such as order bounded operators, cone p-absolutely summing operators and p-majorizing operators, are discussed. In addition, we also provide the modulus and adjoint properties of these two types of operators.
