Iceland in winter

Well, it is possible. I'm not sure what you mean by "lava sites". All of Iceland is a lava site, but there are not many places that have active flowing lava, if that is what you mean. Otherwise, you get to look across vast black emptiness (which is a sight in itself). These are usually summer tours, since the backcountry roads are are often impassable during the winter. The glacier lagoon is the hardest to see, since more tour operators only offer that during the summer. I did find one that I named here, and there may be others. As for everything else, here's one way it could work: 26th: The Blue Lagoon - Relax on arrival at the Blue Lagoon. Flexible arrival/departure times to the Lagoon. End the day walking downtown. Info: http://www.re.is/DayTours/BlueLagoon/Schedule/ 27th: Golden Circle Tour - Hit the three big sights near Reykjavik in one day. 9am to 6pm. End the day walking downtown. Info: http://www.re.is/DayTours/NatureHistory/Details/Golden-Circle/ 28th: Glacier Lagoon Tour + Northern Lights (Depart, 9am)
Info: http://www.extremeiceland.is/en/longer-tours/jokulsarlon-two-day-tour 29th: Glacier Lagoon Tour (Arrive, 9pm-1am) 30th: Depart Island.

"and most important northern lights." Follow the forecast, check this website daily: http://www.gi.alaska.edu/AuroraForecast/Europe/2013/01/05 On a night with a prediction of high aurora activity and clear skies, do the following. Find an area far from the glow of urban lighting, and relatively unobstructed horizons. Dress warmly, grab a folding chair, look towards the sky and wait. I once spent a month in the interior of Alaska during the winter. In 30 days, I saw the lights exactly twice, and both times, I had to make a considerable effort. With only 3 days, to be honest, your chances of seeing the aurora borealis are pretty low.