The train journey takes about 1 hour and 45 minutes and costs NOK 235. You buy the ticket in the airport.  If you buy the ticket on the net, you can get “minipris” which is a much lower price. (http://www.nsb.no/?lang=en_US)

Train departures to Lillehammer from Oslo airport
(arrival in brackets):

Departures Sunday
08:33(10:12), 10:05(11:54), 12:05(13:54), 14:05(15:56), 14:45(16:20), 15:05(16:55), 16:05(17:50), 16:33(18:10), 18:05(19:55), 19:05(21:10), 20:05(21:50), 22:05(23:49), 23,46(01:35)

Departures Monday – Friday
07:05(08:55), 08:05(09:50), 08:33(10:12), 09.05(10:53), 10:05(11:54), 11:05(12:52), 12:05(13:54), 14:05(15:56), 14:45(16:20), 15:05(17:50), 16:05(17:50), 16:33(18:10), 17:05(19:02), 18:05(19:55), 19:05(21:01), 20:05(21:50), 22:05(23:49), 23:46(01:35)    

Departures Saturday
08:33(10:12), 10:05(11:54), 12:05(13:54), 14:05(15:56), 14:45(16:20), 16:05(17:50), 18:05(19:55), 20;05(21:50), 23:35(01:15)

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Train departures from Lillehammer to Oslo airport
(arrival in brackets):

Departures Sunday
07:18 (09:07), 09:13(11:07), 11:10(13:07), 12:58(14:43), 13,16(15:07), 15:09(17:07), 16:20(18,07), 17:14(19:07), 18:11(20:07), 18:46(20:15), 19:20(21:07),  20:05(21:43)

Departures Monday to Friday
04:02(05:45),  04:20(06:06), 05:23(07:07), 06:19(08:07), 07:18(09:07), 08:00(10:07), 08:53(11:07), 10:50(13:07), 11:51(14:07)(not Friday), 12:11(14:07)(only Friday), 12:58(14:43), 13:16(15:07), 14:09(16:07), 15:09(17:07), 16:20(18:07), 17:14(19:07), 18:11(20:07) 18:46(20:15), 19:20(21:07), 20:05(21:43)

Departures Saturday
04:20(06:06), 05:23(07:07), 07:18(09:07), 09:13(11:07), 11:10(13:07), 12:58(14:43), 13:16(15:07), 15:09(17:07), 17:14(19:07), 19:20(21:07), 20:05(21:43)