Requirements for using Schluter Ditra
I would most definitely take up the linoleum. Why? If it starts coming away from the floor substrate (particle board), it could then very well lead to the grout between the tiles cracking (breaking up) due to movement underneath.

Personally I have no time for particle board, therefore would be very! tempted to take it up and replace it with plywood (fixed down appropriately).

That said, according to Schluter-DITRA and Schluter-DITRA-XL: Wood Substrates you can probably get away with keeping the particle board down on the floor. Before commencing I would ensure the particle board is fixed down very! firmly (nailed or screwed @ 150 to 200mm centres). Select a nail or screw length that will not go all the way through the floor boards underneath the particle board, you don't want to go hitting any pipe or cable that might run underneath your flooring.

For total peace of mind I would contact Schluter Systems directly and seek their advice: Contact Schluter Systems