To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function as follows:

- **Variables:**
  - $x_1$: The number of lemons purchased.
  - $x_2$: The number of bananas purchased.

- **Objective Function:**
  The profit from selling lemons is $2 per lemon, and the profit from selling bananas is $1 per banana. Therefore, the total profit can be represented as $2x_1 + x_2$.

- **Constraints:**
  1. The cost constraint: $3x_1 + 1.5x_2 \leq 1000$ (since a lemon costs $3 and a banana costs $1.5, and the total budget is $1000).
  2. The lower bound on lemons sold: $250 \leq x_1$.
  3. The upper bound on lemons sold: $x_1 \leq 300$.
  4. The constraint on bananas sold in relation to lemons: $x_2 \leq \frac{1}{3}x_1$.

Symbolic representation:
```json
{
  'sym_variables': [('x1', 'number of lemons'), ('x2', 'number of bananas')],
  'objective_function': '2*x1 + x2',
  'constraints': [
    '3*x1 + 1.5*x2 <= 1000',
    '250 <= x1',
    'x1 <= 300',
    'x2 <= (1/3)*x1'
  ]
}
```

Now, let's write the Gurobi code to solve this linear programming problem:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=250, ub=300, vtype=GRB.INTEGER, name="lemons")
x2 = m.addVar(vtype=GRB.INTEGER, name="bananas")

# Set the objective function
m.setObjective(2*x1 + x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x1 + 1.5*x2 <= 1000, "budget_constraint")
m.addConstr(x2 <= (1/3)*x1, "banana_lemon_ratio")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of lemons: {x1.x}")
    print(f"Number of bananas: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```