Maybe because log normal can fit easily anything monomodal. On the other hand it would be less suitable if you have some additional agglomeration or fast Ostwald ripening.

this is simplified theory. In practice droplet break-up and coalescence proceeds simultaneously. Simultaneous agglomeration and Ostwald ripening are additional possibilities. Balance under real conditions depends to large extent on the timescale of droplet break-up and adsorption of stabilizers.

One reason for an asymmetrical size distribution can be the average morphology (average because the droplet morphology can fluctuate).  An upper tail can be attributed to elongated structures, whereas spherical structures become closer to unimodal.  A small fraction of droplets fuse into short-lived dimer structures that can also contribute to a log-normal distribution.  In general, the extent of the upper tail distribution can be correlated to the concept of interfacial rigidity.  Less rigid interfaces produce a larger upper-tail distribution and vice versa.  Factors that effect interfacial rigidity include type of surfactant, cosurfactant, and electrolyte interactions for example.

I am not sure how advanced answer you excpect but the simpliest one is that the size of droplets cannot be negative, therefore a symetrical distribution (e.g. the  normal one) cannot be applied. The log-normal function usually describes such distributions very well.

The log-normal distribution was first adopted on empirical basis to avoid direct application of the Gaussian normal law to particle sizes, what was earlier recognized as inconvenient. It can be derived (*) from a kinetic based approach by assuming that times for growth and destruction of particles are normally distributed. The particle growth rate (negative if the particle is shrinking) is considered to be linearly dependent on particle size. The particle size is unrealistically taken as unrestricted by either a minimum or maximum size. Complex physical-chemical phenomena such as particle’s breakup, coalescence, nucleation, or Ostwald ripening, are clearly not adequately accounted for by this highly simplified model. The model suggests a convenient way often used to plot experimental data.

(*) Riyad R. Irani and Clayton F. Callis; “Particle Size: Measurement, Interpretation, and Application”, John Wiley & Sons, New York and London, 1963.

Ostwald ripening (at least in the first stage of the process) and flocculation leads to a bimodal distribution. However, agree that log normal is often a very good approximation.

The log -normal distribution is a statistical method to represent size and size distribution of droplets in emulsion or even powder particles by estimating dm- median particle diameter and σg. ,   dm is diameter corresponding to 50% mass fraction and σ is ratio of diameters corresponding to 84 and 50% of mass. These two parameter represent the size and size distribution of droplets/particles in an aggregate in a log-normal plot. 

 The data are fitted to log-normal to get a straight line which is used to know diameter corresponding to 50 % mass i.e dm and  ratio of d84 and d50 which is σ, standard deviation of size distribution. The log-normal fitting to a straight line facilitate giving these values to represent  size and size distribution.  

it is because almost all datasets are skewed and they have a long tail towards to the right of the mean. we proposed a new solution for skewed datasets.

Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...