Steve J wrote:
I brought my two arum lillies in from the pond in the autumn, and put
them in the unheated conservatory.

Both are now in flower!

Does this mean they won't flower this summer, once I put them back out
on the edge of the pond?

Mine does the same in the same situation. After it has flowered, put it
outside and let it rot down.

When new growth appears in the autumn, bring it back inside again.

Beware of the pollen inside. It can mark.