It seems to me that it should just be 'it seems'.

I agree with Gary: it's probably best just with "it seems." You can also say "it seems like," if you want to soften your accusation a bit, since "seems like" makes your statement a little less definite ("I'm not sure he's lying, but it seems LIKE he is"). Using "it seems that" isn't wrong, but the word "that" is unnecessary and doesn't add anything to the meaning, so it's better to just leave it out.

It is really wrong to go into a store just to humiliate the workers there, which is what this man did. It is not right to lie to people, which is what you just did. I would not use "seem" in these sentences because the actions are pretty clear. For the definitions of "seem": https://www.merriam-webster.com/dictionary/seem