I don't know why people keep getting their knickers in a twist over LIFO. Plain LIFO was tested and found to be discriminatory.
LIFO modified, so that it does not unfairly dismiss a disproportionate number employees who are a minority of the workforce (Race/Gender) has been used legally. It has not resulted in unfair dismissal legal claims for race or sex discrimination. This is important, because such claims have unlimited liability, whereas a plain unfair dismissal claim is capped. Potentially an employer is at liberty to use other criteria, sickness, absenteeism etc., and a bad employer will certainly use this to remove those it dislikes, but if a legal challenge is mounted it can still only be for plain unfair dismissal, for which the max. compensation is peanuts for the employer. (I think its £40k last I looked)