Levene's Test on 2-by-2 Mixed Factor Anova

It is my understanding is that a Levene's test is simply looking at to see whether there are any differences between the differences of the mean. Here is some data:

participant group mean  group.mean  abs.mean.diff
1             a   200     300           100
2             a   300     300             0
3             a   400     300           100
4             b   600     650            50
5             b   700     650            50
6             b   650     650             0


The Levene's test is taking the absolute mean difference (right most column) for each participant, then see whether there is a statistical difference (with an one-anova) between the absolute mean difference when treating group as a factor. My question is if the Levene's test is essentially a one-way anova on the absolute mean difference, can I run a Levene's test on a 2-by-2 anova where I treat group as a between subject variable and condition as a within subject variable?

participant group  condition mean  group.mean  abs.mean.diff
1             a        x      200     250           50
2             a        x      300     250           50
3             a        y      400     500          100
4             a        y      600     500          100
5             b        x      700     675           25
6             b        x      650     675           25
7             b        y      200     150           50
8             b        y      100     150           50