I am not sure where you are pulling the layer definitions from but these are monetary terms not digital asset specific ones. Money scales in layers
Layer 1: The bearer asset with the express purpose of storing value.
Layer 2: The coupon/ currency that is redeemable for the bearer asset on demand from the coupon issuer. (In the case of Lightning the issuer is either the party or counter-party)
Layer 3: The credit token. This historically is where loans and financial stress is added to the lower layers upon calls to redeem. Because the credit tokens by definition create more tokens than assets outstanding. These are based on reputation and trust to create more value than held in the credited currency.
I know that cashu can be minted to layer 1 but it is less secure than lightning so, It is not used that way. Issuing cashu tokens on lighting is creating credit tokens redeemable for lightning/liquid which is then redeemable for bitcoin. There is nothing stopping a mint from issuing more credit that lightning held and redemption is based soley on the reputation and trust in the mint. Cashu is credit.
