Is it considered a lie and forbidden for me to tell my husband, who refuses to let me go out alone, that my brother is with me, while I am actually going out alone due to circumstances?

If the husband has not consummated the marriage with his wife, then she is not obligated to obey him, but rather to obey her guardian (wali). However, if he has consummated the marriage with her, then it is obligatory for her to obey him in what is good and reasonable. She is not permitted to leave his house except with his permission, unless her departure is for a necessity, in which case she is not required to seek his permission.