Of those listed I'd choose "Software Engineering Lead" because there are many types of engineering and also using "Engineering" rather than "Engineer" is a hedge for those without degree for engineers. We had a similar discussion for how to title open positions.
There's no standard afaik, similar to software development vs software engineering. As a reader it would be important to mention if engineering included IT (were you responsible for the office wifi router for example) and team size.
In Germany the equivalent "Leiter" is defined and requires the person to have autonomy over budget and team hiring decisions for example. More like a director. So it's less likely in a startup environment to have that job title. What do startups do? They simply use the english title ;)
