If you only remained in LA for a short time after retiring (or did not intend to stay there permanently), and did not work in LA after retiring, you don't need to file a LA tax return.
If you intended to remain there permanently (i.e. become a LA resident), then any income you earned after retiring is subject to LA income tax. You should file a part-year resident LA tax return to report that income. Any non-military income you earned in LA is taxable in LA.
Military retirement income is exempt from LA income tax, but the correct approach is to file the return to report the income - even if it will get exempted from tax.
