perl -nle "print if /\QLX*\E/ .. /\QCAS*\E/" "filename"

##</code><code>##

LX*
other data
SVC*HC:00003
other data
CAS*
LX*
other data
SVC*HC:00001
other data
CAS*
LX*
other data
SVC*HC:00003
other data
CAS*