It appears that query should work, and what it would do would be to populate the [Lead] column in the Application table with the value of the matching record in the Contacts table [Lead] column if the [Lead] column in the Application table contains some data. Is that what you really want?

The more common situation is to update the Application.Lead column where it contains no data, but if you have a situation where the Contacts table has been updated, and the Application table has not, then your query would be useful. One way to debug this sort of query is to run it as a select query first so you get the set of data you are after, and then change it to an update query.