To solve this optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of acres of carrots grown,
- $x_2$ as the number of acres of onions grown.

The objective function aims to maximize profit, which can be represented as:
\[75x_1 + 90x_2\]

Given the constraints:
1. Tractor time: $1.5x_1 + 2x_2 \leq 120$
2. Hand-picking time: $2.5x_1 + 2x_2 \leq 200$
3. Total land: $x_1 + x_2 \leq 120$

And, of course, $x_1 \geq 0$ and $x_2 \geq 0$ since we cannot grow a negative number of acres.

So, the symbolic representation of our problem is:
```json
{
    'sym_variables': [('x1', 'acres of carrots'), ('x2', 'acres of onions')],
    'objective_function': '75*x1 + 90*x2',
    'constraints': ['1.5*x1 + 2*x2 <= 120', '2.5*x1 + 2*x2 <= 200', 'x1 + x2 <= 120', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="acres_of_carrots")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="acres_of_onions")

# Set the objective function
m.setObjective(75*x1 + 90*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(1.5*x1 + 2*x2 <= 120, "tractor_time")
m.addConstr(2.5*x1 + 2*x2 <= 200, "hand_picking_time")
m.addConstr(x1 + x2 <= 120, "total_land")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Acres of carrots: {x1.x}")
    print(f"Acres of onions: {x2.x}")
    print(f"Maximum profit: ${75*x1.x + 90*x2.x:.2f}")
else:
    print("No optimal solution found")
```