Yes, after the change of variables. Then it’s identical to the Normal GLM. But the cahnge of variables makes it a bit awkward.
The problem is that the linear predictor (or \mu parameter) of the LogNormal is the expectation of, lets say, \log(y). It is not the expectation of y (and \exp(\mu) isn’t either). That can make things weird if your regression parameters have meaning and you want to model expectations. There has been a discussion of this in the trade economics literature which let the whole field to use the Poisson Pseudo Maximum Likelihood (PPML) as the workhorse estimator for gravity models in trade. (In my opinion they should have gone for Gamma GLM, but Gamma GLMs can be numerically unstable.) So although the Gamma and LogNormal distributions can look and behave quite similar, the regression coefficients will generally not be similar, which can lead to a lot of confusion.
Edit: To be clear: I think of GLM as a framework to structure a class or classes of models, which can be extremely helpful. And while you can fit in the LogNormal this framework, I just don’t think it is particularly helpful in this particular case, because the change of the dependent variable is not explicit in this framework (unlike the link function and variance function stuff).