Unfortunately, there is no easy way by public transport from Lisbon Airport to Leiria.
The best option is to take a taxi from Lisbon Airport (There is no Metro Service) to Sete Rios Bus Station and from there catch a Rede-Expressos Coach to Leiria. (Transit time about 2 hours.)
See:
http://www.rede-expressos.pt/
For more info. Note that this site only works on Windows equipped machines with IE5.5 or higher.
For this reason I do not provide timetable info from this site because despite requests for it to be enabled for other browsers there has been no reply from the company on this over seevral months.
This is the best public transport option as travelling by train requires a taxi ride and then a 4 hour trip with 3 changes.
There are certain transfer companies that offer a service including
http://www.low-cost-transfers.com/lisbon-airport/
