Please refer to this blog discusses the issues that may arise when moving, as well as considerations on how to.
How to Migrate SharePoint 2007 to Office 365 Standard Using Native Web Service and CSOM: https://blogs.msdn.microsoft.com/himanshukumar/2012/05/21/how-to-migrate-sharepoint-2007-to-office-365-standard-using-native-web-service-and-csom/
You might want to consider going from SharePoint 2007 -> SharePoint 2010 on-premise -> Office 365. follow this steps:
To do this you can create a SQL backup of the content database and restore it on the SQL server used by SharePoint 2010. Then create a new web app in SP 2010 and attach the copy of the database to this web app. That will upgrade the database to SP 2010.
Now you can use the powershell command to export the list:
export-spweb ... -itemurl <url-to-the-doclib> ...
You can then import the list into the desired site collection using:
Also, Save Document Library as template with content, it will give you .stp file. Follow this steps to convert it to .wsp: http://technet.microsoft.com/en-us/library/cc288476.aspx#STP
Upload it to SP2010 site and Create new document library.
From SharePoint 2010 to Office 365: Save the SharePoint site to template, and then upload it to Office 365 and activate it. Here's an article which will lay out some steps, in which you can save your site as a template and ensure the migration is successful: