The only way you can use limit orders to provide liquidity is to post prices that are the same as the prices of the limit orders, and then you will not be earning any spread. In other words, what you are asking is not possible, since to earn spread you would have to quote a bid that is lower than the price of your client's limit buy order, or an offer that is higher than your limit sell order. This of course runs the very real risk that the client will not get filled on their order, when had their non-discounted interest been advertised to the market, they might have been filled.
Therefore, doing that (spreading the client's order) would be unethical, since you would not be exposing the client's true interest to the market, but rather a discounted interest (unless there exists an explicit understanding between you and your client that you would be acting in this manner). The client has placed their trust in you to execute the order faithfully, and instead you are using the client's interest to earn risk-free profit in a way that jeopardizes their order's execution.