To solve Julia's dietary problem as a linear programming optimization, we first need to define the symbolic representation of the variables and constraints.

Let:
- $x_1$ represent the number of servings of vanilla protein bars consumed.
- $x_2$ represent the number of servings of organic meal replacement shakes consumed.

The objective function aims to minimize the total cost. The cost of vanilla protein bars is $10 per serving, and the cost of organic meal replacement shakes is $15 per serving. Thus, the objective function can be represented algebraically as:
\[ \text{Minimize: } 10x_1 + 15x_2 \]

The constraints based on Julia's requirements are:
1. Protein requirement: At least 155 units of protein.
   - Each vanilla protein bar contains 30 units of protein, and each organic meal replacement shake contains 10 units of protein. Thus, the constraint is $30x_1 + 10x_2 \geq 155$.

2. Carbohydrate requirement: At least 140 units of carbs.
   - Each vanilla protein bar contains 50 units of carbs, and each organic meal replacement shake contains 20 units of carbs. Thus, the constraint is $50x_1 + 20x_2 \geq 140$.

3. Fat intake limit: No more than 55 units of fat.
   - Each vanilla protein bar contains 2 units of fat, and each organic meal replacement shake contains 5 units of fat. Thus, the constraint is $2x_1 + 5x_2 \leq 55$.

4. Non-negativity constraints: Julia cannot consume a negative number of servings of either item.
   - $x_1 \geq 0$
   - $x_2 \geq 0$

In symbolic representation, the problem can be summarized as:
```json
{
  'sym_variables': [('x1', 'vanilla protein bars'), ('x2', 'organic meal replacement shakes')],
  'objective_function': '10*x1 + 15*x2',
  'constraints': [
    '30*x1 + 10*x2 >= 155',
    '50*x1 + 20*x2 >= 140',
    '2*x1 + 5*x2 <= 55',
    'x1 >= 0',
    'x2 >= 0'
  ]
}
```

Now, let's implement this problem in Gurobi using Python:

```python
from gurobipy import *

# Create a new model
m = Model("Julia_Diet")

# Add variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="vanilla_protein_bars", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="organic_meal_replacement_shakes", lb=0)

# Set the objective function
m.setObjective(10*x1 + 15*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(30*x1 + 10*x2 >= 155, "protein_requirement")
m.addConstr(50*x1 + 20*x2 >= 140, "carb_requirement")
m.addConstr(2*x1 + 5*x2 <= 55, "fat_limit")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Vanilla protein bars: {x1.x}")
    print(f"Organic meal replacement shakes: {x2.x}")
    print(f"Total cost: {m.objVal}")
else:
    print("No optimal solution found")
```