Judge Amy McHugh swears in, from left, new council members Logan Brown and Wes Hook, along with returning Council Member Kelly Brynteson, during the City Council meeting on May 18. City of Lakeway The Lakeway City Council on Monday discussed proposals to lower restrictions on special-use permits, required for businesses operating in ways not usually allowed by city code. Businesses within 300 feet of a residential area require a special-use permit.