Heat olive oil in a saucepan over medium heat.
Sauté chopped onions until translucent.
Add chopped tomatoes and cook for about 10 minutes until soft.
Stir in apple cider vinegar, brown sugar, salt, garlic powder, allspice, and black pepper.
Simmer on low heat for 15 minutes, stirring occasionally.
Remove from heat and let cool slightly.
Blend the mixture until smooth.
Return the blended mixture to the saucepan.
Add lemon juice and adjust seasoning to taste.
Cook for an additional 5 minutes to thicken, then let cool before serving.