Heat oil in saucepan. Add onion and saute until softened, about 2 minutes.
Add tomatoes, garlic, 1/4 tsp salt, oregano and basil Simmer mixture about 20 minutes until flavors meld. Remove from heat and cool slightly.
In a food processor place avocado and add tomato mixture. Blend until smooth, about a minute or two. Return mixture to the saucepan and add unflavored almond milk, lime juice and remaining 1/2 tsp salt. Simmer until flavors meld, about 10 minutes. This soup gets even better as it sits, so if you have time, let it stand an extra half hour before serving.