I'm sorry that you're having trouble with the links that should be opening in a Lightbox are opening in a new window on mobile with Safari and Chrome. Would you be able to send us your InDesign layout (or a sample file that recreates the issue) and your html5_output for us to troubleshoot? You can send your files to us here:
You should also be able to use the in5 Hyperlink widget (in5 > Interactive Widgets > Hyperlink) to apply preferences for how a link opens to the selected hyperlink, all hyperlinks, or all text hyperlinks. It adds the target for you based on your selection.
Here's more information: