Is it permissible to write a statement affirming that I have not previously worked in this country, knowing that I have, in order to secure a job that might otherwise go to non-Muslims?

Writing a false declaration is originally considered a forbidden lie, because lying is reporting contrary to reality and leads to wickedness and the Fire. It was the most detestable characteristic to the Prophet, peace and blessings be upon him. However, lying may be permissible if it results in bringing about a considerable benefit or repelling harm from the questioner or others, such as obtaining a job without harming others, or if lying is a means to achieve a right, or if achieving the intended purpose is not possible except through lying, and the purpose is permissible or obligatory. One must beware of lying and use ambiguous statements (ma'arid) whenever possible.