a risk lover agent preferences and the preference of risk natural agent may be the same
Don't commit the cardinal mistake of equating preferences with choices.  

In the context of Expected Utility Theory, the fact that a risk-averse agent ($RA$) would choose $N$ over $M$ implies that 

$$E[u_{RA}(N)] &gt; E[u_{RA}(M)]$$

The fact that a risk-neutral agent ($RN$) could choose $M$ over $N$ implies that

$$E[u_{RN}(N)] &lt; E[u_{RN}(M)] \implies E(N) &lt; E(M)$$

A risk-lover is a person that could choose $M$ over $N$ even if $E(N) &gt; E(M)$. So here that the opposite inequality holds, it is certain that it will also choose $M$ over $N$, given also the fact that there appears to be no other lotteries to choose from. 

But never say that the risk-neutral and the risk-lover have "same preferences". They don't -it just happens, given the available lotteries, that they choose the same lottery, even though they have different preferences.