The first ionization energy is the energy required to remove an electron from a neutral atom in its gaseous phase. The general trend for the first ionization energy is that it increases across a period (from left to right) and decreases down a group.
Thus, the order of first ionization enthalpy for the elements provided, starting from the lowest, is:
\[
\text{Li}<\text{B}<\text{C}<\text{O}<\text{N}<\text{F}
\]
Therefore, the correct order is given by option (3).