Step 1 In a large saute pan over medium heat, combine the onion with the olive oil and cook, stirring occasionally, until the onion is softened and just beginning to caramelize, about 12 minutes.
Step 2 Roughly chop half the figs and add them to the pan. Continue cooking until the figs are just starting to break down, 6 to 9 minutes.
Step 3Add the white wine and one-half cup of the chicken broth to the pan and increase the heat to medium-high. Cook, stirring almost constantly, until the wine and broth reduce to a thick sauce.
Step 4Remove to a food processor or blender and pulse or blend until almost smooth -- there should still be a bit of texture to the salsa.
Step 5Return the salsa to the pan and season to taste with salt and pepper. Halve the remaining figs lengthwise and quarter each half. Add the fig pieces to the pan and heat over medium-low heat until the fig pieces are just warmed, stirring constantly. Thin, if desired, with the remaining chicken broth. Adjust the seasoning and add fresh lemon juice to taste. Serve immediately.