When there is no interaction, can I use multiple comparison such as LSD or Tukey test?

[#1]

I have three factors - Genotype (5 levels), Nitrogen (2 levels), and manipulation (2 levels).

I'm interested in the combination of three factors. I'd like to check how average grain weight responds to defoliation under the different nitrogen conditions. When I analyze it as the full factorial, there was no interaction among genotype x nitrogen x manipulation.

However, I want to indicate the difference in grain weight. So I checked the Tukey test and put the letter on the graph like below.

My question is when there is no interaction, and I used multiple comparisons using Tukey test, how to suggest the p-value of this difference? In this graph, grain weight is greatest in CV2 control under the Nitrogen treatment I, and lowest in CV5 defoliation under the Nitrogen treatment II.

If someone asks me what the p-value of this difference is, how can I present the p-value?

Or, if there is no interaction, the multiple comparisons of the combination is not correct? and only the comparisons per the main factors (which are significant) is correct?

Could you tell me how to compare the mean of combinations when there is no interaction?

Always thanks!!!

[#2]

I generally recommend using post hoc tests after you select the model. Remove terms as indicated by best practices for model selection, and then consider the appropriate tests.

These tests are based on the LS means and the levels associated with specific terms.