As written, the 3 columns of your design matrix are redundant, implying perfect collinearity. This would be a problem for any method, so this must be a misrepresentation of your actual data. To fix this, there must be cases where columns 1 and 2 are both 0, as well as cases where they are both 1. Then the third column will be the product of the first 2 columns. That would resolve the problem.

Three levels of treatment are represented with two dummy variables, because three dummy variables would create perfect collinearity. With three columns, the third is perfectly predicted by the other two. Deleting your third column (but retaining the rows with zeroes in both the first and second columns) resolves the problem. Deleting both the third column and the rows corresponding to the third treatment again creates perfect collinearity, as every case that is not the first treatment is necessarily the second treatment. As in regression, enter two predictor variables in your model to represent the three treatments. The third treatment, where both predictor variables have 0 values, becomes the reference condition. You could also perform the SEM analysis via a multiple populations approach, where each treatment defines a population, and the effect of each treatment is inferred from differences in the mean of the dependent variable across the three populations. I beg pardon for the earlier answer that was entirely off the mark.