There are a variety of ways to deal with multiple objectives, so the answer is "it depends".
Probably the most common approach is to optimize a weighted sum or difference of the individual objective functions (where the weights serve the twin purposes of scaling the individual objective functions to be commensurable and assigning relative priorities). Since you are just replacing one linear objective function with a different (hybrid) linear objective function, lpSolve can definitely handle this.
Another approach, sometimes called lexicographic optimization, assigns preemptive priorities to the individual objective functions. You optimize the highest priority objective first, then lock in the value of that objective and optimize the second highest priority objective, and so on. Not very many solvers support this directly (CPLEX does), and in any case lpSolve does not seem to provide for it. You can still do it, by solving multiple models. After the first model, add a constraint saying that the highest priority objective cannot be worse than its optimal value, and with that added constraint optimize the second highest priority objective. You can do this with lpSolve.
A third approach is to set a cutoff for one objective ("don't do worse than ___") and then optimize the other one. Again, this is straightforward with lpSolve.
So you will need either to figure out weights (first method) or priorities (second and third methods) and maybe a cutoff value (third method), but you can do any of the in lpSolve.