Steam the artichokes over simmering water for @ 20 minutes or until tender.
Cool, slice and reserve.
Clean and de-beard the mussels.
Place 3 cups water and 1 cup white wine over high heat in a large pot fitted with a lid.
Add 1 coarsely chopped onion and 2 ribs chopped celery.
Bring to a boil over high heat and add the mussels.
Cook covered for several minutes until mussels open, tossing and shaking the pot occasionally.
Using a spider wand, remove and reserve mussels to a bowl to cool.
Return the pot to high heat and add the 2 lobsters.
Cook uncovered for 3-4 minutes after the poaching liquid has returned to a boil.
Remove and reserve lobsters to a bowl to cool.
Stain the poaching liquid twice through cheesecloth and once through muslin to clean the broth.
Reserve for another use.
Pop mussel meats from their shells and discard shells.
Reserve meats to a large bowl.
Clean the lobsters of their shells and reserve shells for another use if you like.
Lobster tomalley and roe make great garnishes for this dish so be sure to save those, if you can.
Slice lobster meats and toss with the mussels, artichokes and the remaining ingredients.
Season with salt and white pepper and serve immediately.