No, you won't be able to run LC3 there as LC3 requires PHP and MySQL to run while the hosting plan you refer to doesn't have them.
PHP ver.5.3.0 or higher
GDlib ver.2.0 or higher
MySQL ver.5.0.3 or higher (5.1.31 and higher recommended)
Full requirements for LC3 - http://www.facebook.com/litecommerce#!/notes/litecommerce/litecommerce-30-server-requirements/194738043875336