AUBURN – The city of Auburn and the state will share the cost of the $9.6 million Lake Street Elementary School project. The state is expected to contribute at least 42 percent. If voters approve, another $690,000 may be spent on a larger gym and air conditioning, bringing the total cost to $10.4 million. The additional work will be paid by Auburn only. The state/local share total was incorrectly reported on Thursday’s B1 of the City edition.