To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of interest and then formulating the objective function and constraints using these variables.

Let's define:
- $x_1$ as the number of bottles of Eucalyptus lotion.
- $x_2$ as the number of bottles of Citrus lotion.

The profit from selling one bottle of Eucalyptus lotion is $1, and the profit from selling one bottle of Citrus lotion is $4. Thus, the total profit can be represented by the objective function:
\[ \text{Maximize:} \quad 1x_1 + 4x_2 \]

The constraints are as follows:
1. The store owner does not plan to invest more than $10,000 in inventory. Given that a bottle of Eucalyptus lotion costs $6 and a bottle of Citrus lotion costs $8, the cost constraint can be represented as:
\[ 6x_1 + 8x_2 \leq 10000 \]
2. No more than 1500 bottles of lotion will be sold every month, which gives us the sales volume constraint:
\[ x_1 + x_2 \leq 1500 \]
3. Non-negativity constraints, since the number of bottles cannot be negative:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Symbolic representation in JSON format:
```json
{
    'sym_variables': [('x1', 'Eucalyptus lotion'), ('x2', 'Citrus lotion')],
    'objective_function': 'Maximize: 1*x1 + 4*x2',
    'constraints': ['6*x1 + 8*x2 <= 10000', 'x1 + x2 <= 1500', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Eucalyptus_lotion")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Citrus_lotion")

# Set the objective function
m.setObjective(1*x1 + 4*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(6*x1 + 8*x2 <= 10000, "Cost_constraint")
m.addConstr(x1 + x2 <= 1500, "Sales_volume_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Eucalyptus lotion: {x1.x}")
    print(f"Citrus lotion: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```