Let the prey population be $s$ and the predator population be $l$.
The Lotka-Volterra system follows the following dynamics
$$ \frac{1}{s}\frac{ds}{dt} = r-cl $$
$$ \frac{1}{l}\frac{dl}{dt} = bs-d $$
$r \rightarrow$ Growth rate of prey
$c \rightarrow$ Rate of consumption of prey
$b \rightarrow$ Birth rate of predator
$d \rightarrow$ Death rate of prey
This boils down to,
$$ -\frac{(bs-d)}{s}\frac{ds}{dt} + \frac{(r-cl)}{l}\frac{dl}{dt} = 0 $$
Thus,
$$ \frac{d}{dt}\{d \log(s)-bs + r\log(l) - cl\} = 0 $$
$$ H(s,l) = d \log(s)-bs + r\log(l) - cl $$
$H(s,l)$ remains constant to initial value of $H(s_0,l_0)$ and does not change with time.
If we do a neat trick here, take $q=\log(s)$ and $p=\log(l)$, then $H(s,l)$ can be written in terms of $p,q$, where $H(p,q)$ describes a Hamiltonian system with $p$ as generalized momentum and $q$ as generalized position.