What is the function that describes a sum of lognormal distributions

Question

Let's say that if you have 2 normal distributions, you can find the fit that describes the shape of the distribution by using: $$Y = P1\frac{exp (-0.5({X - µ1})^2)}{\sigma1^2}+P2\frac{exp (-0.5({X - µ2})^2)}{\sigma2^2}$$ Here you can extract the fraction and the mean of each gaussian population in the whole distribution. My question is, how to do the same process with a sum of lognormal distribution described by: $$Y = \frac{1}{X\sigma\sqrt{2\pi}}exp\frac{({lnX- µ})^2}{2\sigma^2}$$