I know how to work from a chemical equation to an ODE, as described here:
http://brunel.ac.uk/~cspgoop/uploads/ode_chemical_network.pdf
How do I go the other way? I want to convert the Lotka-Volterra ODE system to chemical equations so I can use it in a cell simulation program.
This is direct if one analyzes the dynamics Lotka-Volterra systems are supposed to model: some population $X$ of preys, some population $Y$ of predators, in isolation preys reproduce and predators die, and when in contact predators kill preys and multiply.
This fits the system of "chemical" reactions $$X\to2X,\qquad Y\to Z,\qquad X+Y\to2Y,$$ where $Z$ is a junk species accounting for the dead predators.
Minor caveat: the rates $(a,b,c)$ of the three "reactions" above yield the differential equations $$X'=aX-cXY,\qquad Y'=-bY+cXY,\tag{$\ast$}$$ hence, to solve/simulate the general system $$X'=aX-cXY,\qquad Y'=-bY+dXY,$$ depending on four rates $(a,b,c,d)$, one should consider "reduced" populations $$((c/d)X,Y),$$ where $(X,Y)$ solves $(\ast)$.