That does not seem like a valid call to lm(). First, there is no dependent variable in the formula. I would expect something like
model <- lm(y ~ VegetationGrowth + Fire + Rain + Area + Damage * Rain + (1|Site) + (1|Species), data = Vegetation)
so that lm() fits y as a function of all the listed variables.
Second, I do not think that (1|Site) and (1|Species) are valid in lm(). In some other functions like lmer from the lme4 package, that notation allows the model to have a different intercept for every value of Site and every value of Species.
The notation Damage * Rain is valid in lm() and it means the same as
Damage + Rain + Damage:Rain
The damage and Rain terms contribute to the model as normal variables and Damage:Rain designates the interaction of Damage and Rain.
What you have then, is a model that fits some unspecified dependent variable against VegetationGrowth, Fire, Rain, Area, Damage, Rain, and the interaction of Damage and Rain, and the model intercept can be different for each value of Site and Species. As I said, I do not think the varying intercepts are allowed in lm().