Combine all ingredients in a food processor and blend until smooth. If hummus is too thick, add additional lemon juice and olive oil until desired consistency is reached. Store leftover hummus in an airtight container, refrigerated.
For the Sandwiches
On 4 slices of the rye bread, spread about 2 tablespoons of the hummus. On top of the hummus, place the remaining ingredients, divided evenly among each slice of bread. Top with remaining rye bread slice. Cut in half, serve and enjoy!