Freshwater fishing in lakes:

On Bornholm you have both open lakes (you can fish free of charge with the public fishing license) and closed lakes owned by private land owners.

The open lakes on Bornholm you can find here:
https://www.brk.dk/Borger/frivilligkulturogfritid/kulturogfritidstilbud/Friluf
tsliv/Sider/Fiskes%C3%B8er.aspx

Of lakes to me mentioned:
Safirsøen: Pike, perch and carps
Kanegårdsøerne: Pike, perch, eel, tench and carps

There are also Put-and-take lakes, stocked with a variety of different fish. Of these can be mentioned Rainbow trout, zander/walleye, perch, carps, ide/roach, tench, eel and sturgeon.
Aedelfiskens Stenbruds Put-and-Take: http://www.aedelfisken.dk/

Sportdres Trout Lake:
http://www.din-fangst.dk/forside/sportdres-ørredsoe