Optimizing agricultural food production in a nutritionally and environmentally responsible manner can help address global challenges such as climate change and micronutrient deficiencies. However, enhanced methodological approaches, such as nutritional-LCA, are needed for such endeavors. To this end, we test the application of n-LCA with a global case study at the national food supply, food group, and food item levels, by combining food production, trade, environmental LCA, and nutritional databases. Nutritional-LCA is a nascent but important method that integrates nutrition into LCA so that the environmental impacts of food systems can be better represented by accounting for the multi-functionality of food. For this analysis, we use a nutritionally-adjusted functional unit. We calculate metrics related to nutritional quantity at the individual food item and national food supply levels along with metrics that estimate nutritional diversity in a food supply. For this, nutritional estimates of supply are calculated via a trade-weighted matrix by combining regionally-specific nutritional databases with food supply data from FAOSTAT. We estimate environmental impacts, accounting for imports, by attributing regional environmental impacts from a meta-analysis to national food supply. We further explore methodological challenges associated with integrating nutrition into environmental LCA. Examples of such challenges include scaling, weighting, normalization, and absolute vs. relative measures. We find that integrating nutrition into environmental LCA reveals new tradeoffs and greatly affects results. In particular, we find that methodological choice can impact final results and the consequent messages to society, which direct how actors can improve their sustainability.