Combine lemon juice, honey, salt, and water in a saucepan and bring to a boil to create a brine.

Stir in dill.

Pour the hot brine over sliced carrots in a heatproof bowl.

Let the carrots pickle for at least 6 hours, or preferably overnight, in the refrigerator.

Preheat oven to 325°F (160°C).

Melt schmaltz in a skillet over medium heat.

Add sliced onion and salt to the skillet.

Cook onions, stirring occasionally, until softened and browned (about 13 minutes).

Transfer the cooked onions and schmaltz to a food processor; cool completely.

Add chicken livers, eggs, and salt to the food processor.

Puree the mixture until completely smooth.

Pass the chicken liver puree through a fine sieve into a bowl to remove any lumps.

Line a terrine or ramekin with plastic wrap.

Place the lined terrine in a baking dish.

Pour the chicken liver puree into the prepared terrine.

Pour hot water into the baking dish to reach halfway up the sides of the terrine, creating a water bath (bain-marie).

Bake in the preheated oven for 35-40 minutes, or until the pate is set and browned on top.

Remove the terrine from the water bath.

Refrigerate for at least 6 hours to chill the pate thoroughly.

Drain the pickled carrots.

Unmold the pate onto a plate, removing the plastic wrap.

Serve the schmaltzy pate with challah toasts and pickled carrots.