The Wald test is what's used by default for comparing 2 groups of samples in a differential expression analysis.
The LRT is the preferred method for comparing 3 or more groups of samples. For example, say you have 3 groups of samples and you want to see if genes change in expression between any of the groups. When you use the likelihood ratio test, you are doing just one comparison, so it's statistically a more powerful analysis, because you have less of an issue with multiple hypothesis testing.
If you instead do the Wald test on 3 groups of samples, you would need to do 3 separate tests, comparing each group against the other 2. That’s 3 separate analyses, which can create multiple hypothesis issues. In order to avoid these issues, it is advisable to do a likelihood ratio test in experimental setups where you have 3 or more groups of samples.
When running a new analysis, you can set your preferred method in the Differential Expression (DESeq2, compare 2 groups) pipeline under Change Default Options -> Deseq: