LimeWire, by itself, does not need MSINSTIA, the Windows Installer.
Only the installation program needs it, because it is based on the InstallShield install engine, which is now compatible makes uses of the Microsoft Windows Installer core libraries.

I think that you may have a corrupted installation of the InstallShield engine, and it fails upgrading itself automatically.
You should visit the InstallShield support web site to find solutions to your problem.

You may also use the latest version of the Microsoft Registry Cleaner to detect and clean up corrupted Windows components registration. (Warning! don't forget the backup of cleaned entries). One spossible source of problems is that your registry references a component (such as an OCX or shared DLL) which is no more in the registered directory, or that has been renamed or erased.

Check the presence of the VER32.DLL file in the System directory. This file is absolutely required by ALL installation engines on Win32. This file is now part of the core Windows system, but using an outdated version of this file may render some newer versions of installation engines completely inoperable (the Ver32 system library contains functions used to get version information about installed files). Some bogous software come with their own copy of this system file, and overwrite it with an outdated version. This file is most often unused from outside of an installation procedure.

If you have installed Microsoft Office, you may check its components (because Office installs its own installer based on the Windows Installer core engine): click on Help, System Information, then use one of the proposed tools.

This also applies if you have Windows 98SE or ME or XP, because they also provide a version of the MSINFO32.EXE tool used to perform these checks. Then you can run "msinfo32.exe" directly from the Start Menu, Execute command...