To solve the given optimization problem, we will first define the variables and the objective function. Then, we will add the constraints one by one according to the problem description.

Let's denote the quantity of granola bars as `x0`, eggs as `x1`, oreos as `x2`, apple pies as `x3`, lemons as `x4`, and kiwis as `x5`.

The objective function is to minimize: 
`3.55*x0 + 3.57*x1 + 2.41*x2 + 7.83*x3 + 5.78*x4 + 8.69*x5`

We have the following constraints:

* The total amount of fiber from granola bars and lemons should be at least 26 grams: `11*x0 + 32*x4 >= 26`
* The total amount of fiber from eggs and apple pies should be at least 54 grams: `13*x1 + 2*x3 >= 54`
* The total amount of fiber from apple pies and kiwis should be at least 50 grams: `2*x3 + 24*x5 >= 50`
* The total amount of fiber from granola bars and apple pies should be at least 47 grams: `11*x0 + 2*x3 >= 47`
* The total amount of fiber from all items should be at most 327 grams: `11*x0 + 13*x1 + 27*x2 + 2*x3 + 32*x4 + 24*x5 <= 327`
* And the total amount of fiber from all items should also be at least 47 grams (as per another constraint): `11*x0 + 13*x1 + 27*x2 + 2*x3 + 32*x4 + 24*x5 >= 47`
* The constraint: `4*x1 - 6*x3 >= 0` can be rewritten as `4*x1 >= 6*x3` or `2/3*x1 >= x3`
* The constraint: `4*x1 - 6*x5 >= 0` can be rewritten as `4*x1 >= 6*x5` or `2/3*x1 >= x5`
* The constraint: `-8*x1 + 2*x2 + 8*x4 >= 0` can be rewritten as `2*x2 + 8*x4 >= 8*x1`
* The constraint: `27*x2 + 2*x3 + 32*x4 <= 207`

Here is the Gurobi code that captures the problem:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="granola_bars")
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="eggs")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="oreos")
x3 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="apple_pies")
x4 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="lemons")
x5 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="kiwis")

# Set objective function
m.setObjective(3.55*x0 + 3.57*x1 + 2.41*x2 + 7.83*x3 + 5.78*x4 + 8.69*x5, GRB.MINIMIZE)

# Add constraints
m.addConstr(11*x0 + 32*x4 >= 26, name="constraint_1")
m.addConstr(13*x1 + 2*x3 >= 54, name="constraint_2")
m.addConstr(2*x3 + 24*x5 >= 50, name="constraint_3")
m.addConstr(11*x0 + 2*x3 >= 47, name="constraint_4")
m.addConstr(11*x0 + 13*x1 + 27*x2 + 2*x3 + 32*x4 + 24*x5 <= 327, name="constraint_5")
m.addConstr(11*x0 + 13*x1 + 27*x2 + 2*x3 + 32*x4 + 24*x5 >= 47, name="constraint_6")
m.addConstr(4*x1 - 6*x3 >= 0, name="constraint_7")
m.addConstr(4*x1 - 6*x5 >= 0, name="constraint_8")
m.addConstr(-8*x1 + 2*x2 + 8*x4 >= 0, name="constraint_9")
m.addConstr(27*x2 + 2*x3 + 32*x4 <= 207, name="constraint_10")

# Optimize model
m.optimize()

# Print results
for v in m.getVars():
    print('%s %g' % (v.varName, v.x))
```