Spray 3-cup soufflé dish or terrine with vegetable oil spray. Line dish with plastic wrap; spray plastic.
Combine chicken livers, broth and onion in medium saucepan. Bring to boil. Cover and simmer until livers are cooked through, stirring occasionally, about 12 minutes.
Drain cooking liquid; transfer chicken livers and onion to processor.
Add butter, Cognac and salt to processor. Puree until smooth.
Transfer to prepared dish. Cover and refrigerate until firm, at least 4 hours.
Bring wine to simmer in small saucepan.
Remove from heat.
Add figs.
Let stand until figs soften, about 15 minutes.
Drain wine. Quarter figs. (Pâté and figs can be prepared 1 day ahead. Keep pâté refrigerated.
Transfer figs to small bowl; cover and refrigerate.)
Unmold pâté onto platter. Press walnuts onto sides of pâté.
Garnish top with chives and some figs. Arrange lettuce on platter with pâté.