Even the year of birth is speculated on the basis of an incident he recounted of a dinner in Madikeri in 1803 hosted by Veer Rajender Wadeer, the ruler of the province of Coorg.

Observing a solar eclipse through the telescope of a theodolite without darkened glasses led to the burning of the retina of his left eye.

After this accident he obtained with the help of his friends, especially Sir Brook Watson, an appointment as barrack-master in New Brunswick with a salary of 400 pounds per year.

He was also able to demonstrate his skills in navigating by the stars during the campaign and had prevented a critical error when General Baird was headed in the wrong direction while attempting to get around Tipu's camp at night.

[7] After the capture of Mysore, Lambton proposed to Wellesley that the territory be surveyed, using the new techniques of geodesy employed by William Roy in Great Britain.

Lambton's proposal was however examined by Nevil Maskelyne, Astronomer Royal and a relative of Lord Clive.

[8] Just around the time that Lambton got his survey approved by Lord Clive, he happened to hear of some instruments being carried back from China by astronomer Dr. James Dinwiddie.

They then triangulated their way to Bangalore where the 1804 baseline was measured by John Warren to check the survey accuracy (also examining the errors introduced by refraction[11]).

[14] Lambton essentially followed a system established in England by General Roy for the Principal Triangulation of Great Britain.

In the earliest surveys conducted in Bangalore he noted:[9][15] But should the earth prove to be neither an ellipsoid, nor a figure generated by any particular curve, of known properties, but a figure whose meridional section is bounded by no law of curvature, then we can obtain nothing until we have an actual measurement, to be applied as has been already mentioned.The Bangalore baseline of 1800 made use of a chain laid in long coffers supported on pickets and the heads were aligned using a telescope.

The subsequent baselines including were made more carefully with the use of a Ramsden's chain specially calibrated for tropical temperatures, consisting of 40 links of 2.5 feet (0.76 m) each and measuring 100 feet (30 m) at 62 °F (17 °C), and a boning telescope (a small, low-magnification telescope used for aligning the tops of survey poles).

[16][17] He took special precautions to account for the expansion of the chain under the Indian weather; and repeated measurements with rotations of the telescope of the Zenith sector so as to account for collimation errors in determining the latitude (the elevation of the pole star directly provides the latitude but owing to errors related to determining the horizon and from refraction, the preferred method in surveying was to use well known stars located closer to the zenith, such as Aldebaran for India, whose declination from the pole-star had been pre-established).

Lambton's assistant John Warren investigated the effect of refraction on errors in calculating the latitudes.

[18][9] The main survey instrument from 1802 for the primary triangles was a Great Theodolite made by William Cary.

[15] Lambton was made a Fellow of the Royal Society (9 January 1817)[19] and a corresponding member of the French Academy of Sciences in 1817.