Lax matriculated in the Michaelmas term of 1781 and became a private tutor to John Pond, later Astronomer Royal. Lax was elected a scholar (i.e. one on a scholarship) of Trinity in 1784; John Cranke and Henry Therond were his tutors, a role which would have seen them not only teaching Lax, but also acting in the role of "in loco parentis". Lax was conferred a Bachelor of Arts (B.A.) in 1785 and graduated as the Senior Wrangler and was awarded the first Smith's Prize of his year. Until 1790, all examinations at Trinity were written in Latin. In 1785 Lax was appointed curate of Tideswell in the Peak District of Derbyshire with an annual stipend of £35. In 1786, as was essentially the due of Senior Wranglers, he was elected a fellow of Trinity College. According to Peter Linehan, fellows at this time, "were becoming richer, living and behaving more like gentlemen". He was ordained as a minister in 1787 at Peterborough and received his Master of Arts (M.A.) in 1788. He was a moderator from 1789 to 1791 which entailed him presiding over oral examinations which were then necessary for the B.A. to be awarded. As a moderator Lax was responsible for the introduction of "very high flown compliments, and at the same time extending the disputations to double the usual length, which was around one hour and ten minutes" which "sent a ripple through tradition" according to Greg Dening. Dening argues that this was, "Lax's way of getting into the act and making Acts flourish". In 1791 he was appointed as a taxor by the University. Lax was an assistant tutor from 1797 until 1801, but resigned when he married Margaret Cradock, as College fellows were not permitted to marry. In 1795 Lax was appointed Lowndean Professor of Astronomy and Geometry in succession to John Smith. The position was a sinecure with an annual salary initially of around £300, later rising to around £500 per annum by 1821. Cambridge had two astronomical chairs, and the Lowndean was seen as the more theoretical and less experimental of the two. During Lax's tenure a mathematical chair was seen as "a prize or a means of securing leisure, and at best, merely as offering a position where a man could pursue his own researches undisturbed by other duties".