Many of our SharePoint 2013 list forms have been customized with InfoPath Designer. When our lists are automatically migrated to SharePoint Online without Forms Service installed, will the customized list forms continue to display as modified with InfoPath? If not, how will they display? I mean, will they revert to a default SharePoint list layout (one column per displayed row on the form) or will they retain any of the custom layout and design elements?
If you are migrating using any 3rd party tool (e.g. Sharegate), then the migration tool does the InfoPath migration(publishing to SP Online). Sharegate will ensure all the Data Connections used in the InfoPath are converted to the SP Online URL's.
If you are not using any 3rd party tool, in that scenario, your lists need to be created manually (or by any automated script using CSOM) at the SP Online end and data migration done using MS Migration API's. In this particular scenario, since you are creating the lists manually, the display elements will be reverted back to default SharePoint list layout. The InfoPath migration in this case has to be done manually ( involves a lot of effort :( )