I have an experimental setup of bulk RNAseq with a control group n = 6, and condition group n = 1. It was impossible to get more than one sample for the condition, it is unique. I am using DESeq2 for DGE identification and clusterProfiler for enrichment analysis. I know DESeq2 would calculate dispersion per gene based on my control group and I can run the normal workflow, however I was wondering if there are any guidelines for pvalue and LFC cutoffs for such a setup?

I am working with axolot, and the fact that not all genes can be used for downstream analysis as not all would map to any usable ID's makes it so that the results of GO / KEGG while have similar overall tendencies still skew quite a lot. Please help me find the best practice here.

There is nothing special about your situation. There is no general consensus on cutoffs other than the commonly used pad<0.05. It's on you what you use as cutoffs.