If an increase in consumer income causes a decrease in demand for lard then lard is considered an inferior good. This is because the income elasticity of demand is negative. Think, for example, of your demand for public transportation. As income increases, consumers demand less public transportation because they can afford taking an Uber or can afford to drive their own car. If the income elasticity of demand were positive, then an increase in income for lead to an increase in demand. This would be the case for private transportation (car ownership). As income increase, individuals demand more (and higher quality) cars.