The spreading of cancer cells, also known as metastasis, is a lethal hallmark in cancer progression and the primary cause of cancer death. Recent cancer research has suggested that the remodeling of collagen fibers in the extracellular matrix (ECM) of the tumor microenvironment facilitates the migration of cancer cells during metastasis. ECM remodeling refers to the following two procedures: the ECM degradation caused by enzyme matrix metalloproteinases and the ECM alignment due to the cross-linking enzyme lysyl oxidase (LOX). Such modifications of ECM collagen fibers result in changes of ECM physical and biomechanical properties that affect cancer cell migration through the ECM. However, the mechanism of such cancer migration through a remodeling ECM remains not well understood. A mathematical model is proposed in this work to better describe and understand cancer migration by means of ECM remodeling. Effects of LOX are considered to enable transport of enzymes and migration of cells through a dynamic, reactive tumor microenvironment that is modulated during cell migration. For validation cases, the results obtained show comparable trends to previously established models. In novel test cases, the model predicts the impact on ECM remodeling and the overall migration of cancer cells due to the inclusion of LOX, which has not yet been included in previous cancer invasion models.