The English Naval Infantry, which may be viewed as the forerunner of the Royal Marines, was founded in 1664. The Marines were founded in 1755.
In the Royal Navy of Jane Austen's period, the rank of Lieutenant would have been a fairly senior one. Lieutenants usually began their shipboard careers as young boys known as Midshipmen. They often came from wealthy families, and had to pass examinations in order to be promoted. However, a 'Lieutenant of Marines' may have followed a different career path.