Hi, most reservations will not be open yet now.
From Lille I would suggest to travel with Belgian IC trains (reservation not needed) to Brussel and from there German ICE trains to Cologne and change there to ICE to Hamburg.
You can also travel via Antwerp and The Netherlands to Hamburg. Reservation not needed, except optional in IC Amsterdam-Berlin and ICE. I would suggest to not use Thalys (reservations are very expensive).
From Hamburg IC trains to Copenhagen and Öresundbridge trains to Malmö and SJ Highspeed train to Stockholm or Nighttrain directly Hamburg-Stockholm.
For German Trains (ICE, IC Amsterdam-Berlin, IC and EC in Germany) you can reserve via Deutsche Bahn a Family Reservation, but it is optional. For trains to Copenhagen reservations are not open yet.