Title on resume - need advice

Resume/title advice please. In my industry/function, a Manager/Sr Manager title carries more weight/clout than a Lead title. However, at my current company, I'm a Lead, which is a step up from a Sr Manager, and considered a junior Director. I'm also a people manager. I don't think companies I'm applying to will understand a Lead title, and this is specific to this current company (does not translate into the larger industry). Is it ok to put Senior Manager on my resume, (technically a step below what I am) or should I put Lead/Senior Manager and speak to it if necessary?