Would Expense or Liability account for IOLTA bank be better when transferring money to Operating bank?

That is a very good question, because normally you can use a 'transfer' to record the movement of funds from one account to another.  However, this doesn't work with an IOLTA account.

When funds are deposited into an IOLTA account, they should be credited to a Liability account.  The balances on the two accounts should always be equal (opposites).  The bank account will be a debit balance, and the liability an equal credit balance.

When transferring, the best practice is to record a 'check' or 'expense' transaction to credit the bank balance and debit (reduce) the liability account.  When recording the money into the account receiving the funds, the bank would be debited and the credit would be to an income account.

Depending on the number of individual funds in an IOLTA account, you can also create a special report to show a list of the funds individually.

I hope this helps... if not, please feel free to reach out.  :-)