If everything required to complete the publication process has been received, it can take as little as two weeks before your app is available in the app stores. However, more time maybe required for large keys with complex media requirements or extensive app customizations. You should also factor time for testing your app prior to its public release in the app stores. This can take anywhere from a few days to weeks.
Key publication is also subject to review processes by Google and Apple, normally this only takes a couple of days, but can take longer.
The Lucid team should be able to give you an estimate on publication time once all the files and information has been submitted.