Lotteries don’t allow the participant to influence the outcome nor have the winners of a lottery preformed at a level to distinguish themselves relative to others.
Suggesting it’s a lottery diminishes those that gain acceptances and suggests that something in their application of performance didn’t distinguish them but instead luck prevailed. Candidates that don’t get accepted are no less worthy but the results aren’t totally random like a lottery and the analogy suggests a degree of passivity in outcome that is not supported by experience or fact.
Knowing a person here or there that might suggest a narrative is anecdotal at best. The reality is that the top tier of RD students typically have several schools to choose from suggesting results that support a meritocracy of sorts while some randomness clearly exists.
Communicating to the OP that it is a lottery insults all of the daughters achievements to date and falsely implies that she lacks the ability to further impact her chances.
OP encourage your kid, she is a great candidate. There are clearly no guarantees and she should find some safe schools with good fit but keep up the excellent work!!