Can LiteSpeed be installed on a server having both 32-bit and 64-bit versions of SQL Server?
LiteSpeed version 4.7.0.00096 or later is able to be installed for a machine having 32-bit and 64-bit SQL Server nodes.
Install LiteSpeed with 64bit installer (LiteSpeed-x64.msi).
Run the 64 bit installer (LiteSpeed2005-x64.msi) on the server. It will automatically detect and install the corresponding executable to the appropriate bit version of SQL Server instances.