InnoDB Transactional Databases
From Lunarpages Web Hosting Wiki
Do you offer transactional databases such as InnoDB?
Yes, we do support transactional databases. InnoDB tables in MySQL are supported on our LPCP servers. If you have an existing account on a cPanel server and require InnoDB please contact email@example.com to have your account moved to a LPCP server.
PostGRES databases are supported on all shared Linux servers (Basic and Business plans).
Magento: If you are inquiring about InnoDB in regards to installing the Magento shopping cart, all LPCP servers have an auto installer for this shopping cart called Softaculous.