Just checked. Only opens Sunday 11am-3pm.
Red House Farm between Lymm and Broadheath is another option.
Or Lavender Barn Tea Rooms in Dunham
Both cycle friendly too (although I have never been but my cycling club stops there).
Oh, and there's a reasonably new garden centre opened, Lymm Nurseries on Rushgreen Rd In Lymm. They have a cafe and can't imagine them being unfriendly.
There is a sign on the TPT as you are approaching Lymm for a cafe (can't remember the name). Somewhere near the Co-op I believe.