Error in differentiating `inv`(matrix) with LAPACK function `getrf!`

When using Trixi.jl with Enzyme.jl's automatic differentiation, I encountered an error with LAPACK's `getrf!` function:

```
ERROR: No augmented forward pass found for dgetrf_64_
```

The error occurs in the following function from Trixi.jl (src/solvers/dgsem/basis_lobatto_legendre.jl:771): https://github.com/junyixu/TrixiEnzyme.jl/issues/1#issuecomment-2580639062

I've distilled the problem into a minimal working example:

## MWE
```julia
using Enzyme

# Helper function for Legendre polynomials
function legendre_polynomial_and_derivative(n, x)
if n == 0
return 1.0, 0.0
elseif n == 1
return x, 1.0
end

p_prev = 1.0 # P₀(x)
p = x # P₁(x)
dp_prev = 0.0 # P₀'(x)
dp = 1.0 # P₁'(x)

for i in 2:n
p_new = ((2i-1)*x*p - (i-1)*p_prev)/i
dp_new = ((2i-1)*(p + x*dp) - (i-1)*dp_prev)/i
p_prev, dp_prev = p, dp
p, dp = p_new, dp_new
end
return p, dp
end

# Main function to test
function vandermonde_legendre(nodes, N::Integer)
n_nodes = length(nodes)
n_modes = N + 1
vandermonde = zeros(n_nodes, n_modes)
for i in 1:n_nodes
for m in 1:n_modes
vandermonde[i, m], _ = legendre_polynomial_and_derivative(m - 1, nodes[i])
end
end
return inv(vandermonde) # only return inverse for simplification
end

# Test function using vandermonde_legendre
function f(x)
nodes = [-1.0, 0.0, 1.0] # fixed nodes for testing
V_inv = vandermonde_legendre(nodes, 2)
return sum(V_inv) # return scalar output
end

# Try automatic differentiation
x = 1.0
result = autodiff(Reverse, f, Active, Active(1.0))
```

## Environment
```julia
Enzyme v0.13.24
Trixi v0.9.13
```

I noticed a similar discussion in #1820 about LAPACK functions. Would defining custom Enzyme rules be a solution here, or are there other recommended approaches for handling LAPACK functions in automatic differentiation?