New polling shows that Ms Lake, a key Trump backer in the state, has been unable to win over 17 per cent of voters who intend to support the former president in November.
These voters instead look set to split their ticket and vote for her Democrat challenger.
The rise of moderate and sceptical Republicans splitting their ticket in Arizona threatens Ms Lake's campaign, in which she is running to replace the incumbent independent senator Kyrsten Sinema.
The Democratic candidate, Ruben Gallego, is more than ten point ahead of Ms Lake in the latest poll, conducted for Fox News.