Sum of Log-normal and exponential random variables

Question

I have two random variables X and Y. X is lognormally with pdf f(x) and CDF F(X), whereas Y is exponentially distributed with pdf g(y) and CDF G(y). In my application, I need to calculate CDF H(z) of Z = X+Y. I know one standard way that is mentioned widely in the books is convolution of X & Y i.e. \begin{align}H(z) = \int_{-\infty}^{\infty} F(z-y)g(y)dy \end{align} Are there any assumptions involves while evaluating this integral. Because in another application I tried to convolute gamma and exponentially distributed RVs, and depending on the value of parameters for distributions sometimes the result of integration was an imaginary number. This happened because in those cases scale parameter of gamma distribution was negative. So, I would like to know that is it mathematically possible to convolute X & Y as defined above.