The confusion is understandable, especially if you are not overly familiar with mod_perl. Essentially, cpan has determined that Apache is a prerequisite for SOAP::Lite and that since the Apache module is part of the mod_perl dist, that's what it tries to install. Your package manager shows that you have the vendor's mod_perl already, but that is mod_perl2 and it uses the Bundle::Apache2 metamodule and namespace which is quite different from Apache (the 2 is part of the module name, it's not really a version number. I did say it was confusing).

TBH, I don't see why cpan is seeing Apache as a prerequisite of SOAP::Lite and am 100% sure that I have installed the latter without the former in the past. I suggest that you try to install SOAP::Lite by hand and (if you like) use cpan to install each prerequisite independently, but ignoring Apache as such. If you aren't going to be running SOAP::Lite on the server side, you won't need it anyway.

See the mod_perl site for details of the renaming from 1 to 2 if you are so inclined.