Does anybody know where I can find information on migrating a custom theme from version 6.1.5 to version 7?
You can find information regarding that topic in the portal wiki.
Your migration path depends on what kind of theme you were using. In 6.1.5 there was an old theme and page builder theme. I guess with custom theme you are refering to the old theme that was available in 6.0.x and 6.1.x..
For the old themes created with the RAD check: http://www-10.lotus.com/ldd/portalwiki.nsf/dx/Migrating_themes_wp7
For the old pagebuilder theme check: http://www-10.lotus.com/ldd/portalwiki.nsf/dx/Moving_a_mashup_theme_to_the_new_architecture_wp7