With the prevalence of degenerative diseases due to the increase in the aging population, we have encountered many spine-related disorders. Since the spine is a crucial part of the body, fast and accurate diagnosis is critically important. Generally, clinicians use X-ray images to diagnose the spine, but X-ray images are commonly occluded by the shadows of some bones, making it hard to identify the whole spine. Therefore, recently, various deep-learning-based spinal X-ray image analysis approaches have been proposed to help diagnose the spine. However, these approaches did not consider the characteristics of frequent occlusion in the X-ray image and the properties of the vertebra shape. Therefore, based on the X-ray image properties and vertebra shape, we present a novel landmark detection network specialized in lumbar X-ray images. The proposed network consists of two stages: The first step detects the centers of the lumbar vertebrae and the upper end plate of the first sacral vertebra (S1), and the second step detects the four corner points of each lumbar vertebra and two corner points of S1 from the image obtained in the first step. We used random spine cutout augmentation in the first step to robustify the network against the commonly obscured X-ray images. Furthermore, in the second step, we used CoordConv to make the network recognize the location distribution of landmarks and part affinity fields to understand the morphological features of the vertebrae, resulting in more accurate landmark detection. The proposed network was evaluated using 304 X-ray images, and it achieved 98.02% accuracy in center detection and 8.34% relative distance error in corner detection. This indicates that our network can detect spinal landmarks reliably enough to support radiologists in analyzing the lumbar X-ray images.