If its a through ticket EI/MH as long as you have a ticket number and its visable in CMT then your ok. The prefix of the ticket number will either be 232 ( MH ) or 053 ( EI ) . Usually its the former.
Not being able to view on EI.COM is normal on these kinds of tickets. If in doubt call Aer Lingus and check with them they have the ticket number for the DUB-LHR.