To elaborate on coinfrogs response ... (maybe TMI

)
The specification for a 1942
Lincoln Cent mass was 3.11 grams, with a tolerance of 0.13 g. That puts the lower limit of the specification at 2.98 grams, and makes your coin potentially 6% below tolerance.
So ...
1. How did you weigh it, were there any additional decimal places, and if so, what were they? If you have a good balance, and the weight was 2.83 g. now we are talking about only 5% underweight (yes, it matters).
2. There is some metal loss on the rim at 12:00-1:00 (referenced to the obv). Probably only a couple of percent, but that could contribute
3. Wear is unlikely to account for more that 5% weight loss (so, maximum of 0.15 g). But between the metal loss and wear, we could be close to 2.8 g., however ...
4. Atmospheric corrosion ADDS weight. Verdigris, which appears to be present on the reverse, adds 75% to the weight of copper. But it is only affecting a small surface layer, not the entire mass of the coin. ANd you've also got some black gunk (copper oxides?) adding rather than subtracting weight on the reverse, but it looks like someone has cleaned off some of it on the obverse, which again, could take away some metal.
So, still the best bet is that you've got metal loss due to damage, plus wear, reducing the weight of a coin that was below target to start with. The only way to test your alloy theory would be to run XRF and see if the allow is less than 95% copper.