When you connect to your Pi from another Linux machine running X, you don't need to run either startlxde or startx. You are using ssh -X to log in to your Pi, you are using X11 forwarding. You should be able to run any X application on your Pi and the window will appear on your desktop Linux machine. For example, you should be able to run pistore.
Linux Mint already has a Display Manager/Window Manager running on the X11 server (the default is MDM I believe). By running startlxde you are trying to start another Display Manager. There can only be one display manager active at a time. When using Xming you can run in different modes (http://www.straightrunning.com/XmingNotes/manual.php
), some of these modes allow you to run an external Display Manager, others don't.