You can use onMouseIn on the button for the opening of the lightbox and this will work fine on desktop devices.
You will need to use the lightboxes own close or x buttons to close the lightbox or add your own through the use of code on the lightbox itself.
You can’t use the onMouseOut with the button to close the lightbox on the page as the button will be hidden by the lightbox and its overlay.
As onMouse won’t work with mobile devices, you can use the Wix Window API and the formFactor to do code for a certain type of device only.
https://www.wix.com/corvid/reference/wix-window.html#formFactor
https://support.wix.com/en/article/corvid-writing-code-that-only-runs-on-mobile-devices
https://support.wix.com/en/article/corvid-tutorial-displaying-elements-in-mobile-only