Correct Answer: To resize a Logical Volume (LV) named lv1 under Volume Group (VG) vg0 from 100MB to 500MB without losing data and to make the change online, you follow these steps: First, verify the current size of your Logical Volume using the command 'lvdisplay /dev/vg0/lv1'. Then, use the command 'lvextend -L 500M /dev/vg0/lv1' to extend the Logical Volume size to 500MB. To apply the new size to the filesystem without unmounting it, you can use 'resize2fs /dev/vg0/lv1' if it is an ext2/ext3/ext4 filesystem. Finally, verify the new size using 'lvdisplay /dev/vg0/lv1' and 'df -h' commands to ensure the Logical Volume and the filesystem reflect the new size.