There shouldn't be any problem installing LJ on a 5.6+ SME box. I haven't done so, but having a quick look at the requirements it looks like it shouldn't be a problem.
The one thing you will need to look at are the Perl Modules:
DBI libdbi-perl
DBD::mysql libdbd-mysql-perl
Digest::MD5 libdigest-md5-perl
Image::Size libimage-size-perl
MIME::Lite libmime-lite-perl
MIME::Words libmime-perl
Compress::Zlib libcompress-zlib-perl
MIME::Base64 libmime-base64-perl
URI::URL liburi-perl
HTML::Tagset libhtml-tagset-perl
HTML::Parser libhtml-parser-perl
LWP::Simple libwww-perl
LWP::UserAgent libwww-perl
Mail::Address libmailtools-perl
Unicode::MapUTF8 libunicode-maputf8-perl
Storable libstorable-perl
I have all of these on my boxen, but they may not have come stock with SME, but there are rpm's available. Mod-perl will be the biggie.