You can also fly to Sandefjord Airport Torp, Norway.
The low-cost airlines Ryanair and Wizzair fly to the  Sandefjord Airport Torp.
From Sandefjord Airport, there is train service to Lillehammer. At the airport, there is a shuttle bus to the railway station free of charge. Take the bus marked “Tog mot Oslo”.

Once you board the train at the Sandefjord Airport station (Sandefjord Lufthavn Torp), you can take it through Oslo all the way to Lillehammer, so you do not have to change trains. The train journey takes about 4 hours and 15 minutes and costs NOK518. You buy the ticket in the train.  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 Sandefjord Airport Torp
(arrival in brackets)
Departures Sunday
07:41(11:54), 09:41(13:54), 11:41(15:56), 12:41(16:55),  13:41(17:50), 15:40(19:55), 16:40(21:01), 17:40(21:50), 19:41(23:49), 20:41(01:35)

Departures Monday to Friday
04:42(08:55), 05.42(09:50), 06:07(10:12), 06:42(10:53), 07:41(11:54), 08:41(12:52), 09:41(13:54), 11:41(15:56), 12:41(16:55), 13:41(17:50), 14:41(19:02), 15:40(19:55), 16:40(21:01), 17:40(21:50), 19:41(23:49), 20:41(01:35)

Departures Saturday
07:41(11:54),  09:41(13:54), 11:41(15:56), 13:41(17:50), 15:40(19:55), 17:40(21:50), 19:41(23:49)

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Train departures from Lillehammer to Sandefjord Airport Torp
(arrival in brackets)
Departures Sunday
07:18(11:28), 09:13(13:28), 11:10(15:28), 13,16(17:28), 15:09(19:28), 16:20(20:28), 17:14(21:28), 18:11(22:28)

Departures Monday to Friday
04:02(08:28),  05:23(09:28), 06:19(10:28), 07:18(11:28), 08:00(12:28), 08:53(13:53), 09:13(13:28), 10:50(15:28), 11:51(16:28)(not Friday), 12:11(16:28)(only Friday), 13:16(17:28), 14:09((18:28), 15:09(19:28), 16:20(20:28), 17:14(21:28), 18:11(22:28), 19:20(23:23)

Departures Sunday
07:18(11:28), 09:13(13:28), 11:10(15:28), 13:16(17:28), 15:09(19:28), 17:14(21:28), 18:11(22:28), 19:20(23:23)