If I present my duty free LAG items in their sealed bag, are they guaranteed to be cleared? What does 'to be cleared' mean in this sentence? Thanks.

If LAG means La Guardia Airport, then "to be cleared" probably means gets through customs with no problem.  It is not a guarantee, however, as you may be exceeding the amount you can bring into the country. There is a limit on how much of  many things you can bring into a country without tax, like alcohol, tobacco etc.