I found the answer in: https://machinelearningmastery.com/linear-discriminant-analysis-for-machine-learning/
Making Predictions with LDA
LDA makes predictions by estimating the probability that a new set of
inputs belongs to each class. The class that gets the highest
probability is the output class and a prediction is made.
The model uses Bayes Theorem to estimate the probabilities. Briefly
Bayes’ Theorem can be used to estimate the probability of the output
class (k) given the input (x) using the probability of each class and
the probability of the data belonging to each class:
P(Y=x|X=x) = (PIk * fk(x)) / sum(PIl * fl(x))
Where PIk refers to the base probability of each class (k) observed in
your training data (e.g. 0.5 for a 50-50 split in a two class
problem). In Bayes’ Theorem this is called the prior probability.
PIk = nk/n
The f(x) above is the estimated probability of x belonging to the
class. A Gaussian distribution function is used for f(x). Plugging the
Gaussian into the above equation and simplifying we end up with the
equation below. This is called a discriminate function and the class
is calculated as having the largest value will be the output
Dk(x) = x * (muk/siga^2) – (muk^2/(2*sigma^2)) + ln(PIk)
Dk(x) is the discriminate function for class k given input x, the muk,
sigma^2 and PIk are all estimated from your data.
So yes, it uses Bayes Theorem to estimate the probabilities.