What do teaching faculty do during semester breaks? I'm specifically asking about full-time teaching staff (unlike part-time teaching staff such as professors, who as I understand it can just spend more time on research during semester breaks).

I understand US universities pay their professors only 9 months a year, which effectively means they're free to do whatever they want in the remaining 3 months. Does this apply to lecturers too? If so, since professors acquire funding so they can continue to draw a salary during these 3 months, do lecturers also have funding targets? In that case, are they even full-time teaching staff (since they also have to do research to actually acquire funding)? 

What about non-US universities where staff are paid for the entire year?

From what I know about high school, there are some duties that teachers must do during the semester breaks (such as grade exam papers &amp; discuss what to teach next year), but they are few. Once these duties are done then teachers have no duties - they don't have to show up to school - so they usually take the chance to go on holiday. However, at least in the high school I studied in, these periods are short - there's a maximum of 2 months of teaching downtime in the academic year (this neglects the afore-mentioned time taken to grade exam papers etc), which is well below the downtime at university. Surely lecturers don't just go on holiday for 3 months (they must run out of annual leave)? But if they don't go on holiday, what do they do?
In the United States, the "9 month salary" for a faculty member is typically paid out over 12 months.  For those faculty who engage in research or other pursuits during the summer months, the "9 month" designation gives the rate at which their salary can be enhanced through external funding.

So, what do "full time teaching" faculty do over the summer?  Colleagues of mine in such positions generally still look at this time as an opportunity to focus on their professional interests, whether that is doing research or some other field-appropriate equivalent such as writing books, directing theatrical performances, etc.

Teaching responsibilities may also extend through the summer (and may be additionally compensated or not, depending on circumstances). Examples include teaching summer courses, preparing new course material, and supporting student groups' activities (summer is a common time for technical competitions, for example).

And some, in some circumstances, really do just take the summer slowly. In my experience, though, that tends to be the exception rather than the rule, with so many other opportunities and responsibilities at hand.