What is the probability projected LTV becomes actual LTV?
The answer is it really depends.
The projection models are statistical tools for you to analyze trends in your data and extrapolate future values based on those trends. The less complete your dataset is, the more likely that model will be incomplete or miss key days that impact the extrapolation.
Consider trying to estimate the weight of a child at its first birthday based on its weight over the first few days after being born. You can certainly extrapolate the data to estimate a weight, but including additional days and weeks will likely provide better data set to extrapolate and estimate from.
A sample projection model.