I don't think pH 7.0 is your real problem. It is not ideal for peppers, so if you are trying to maximize yield you will want to fix it. For a casual grower, or an in-ground grower, I would say 7.0 is acceptable, and it certainly isn't high enough to lock out nutrients. If your lime is Calcium based and you use a lot of it, you may get Magnesium lockout because Mg is at the back of the line in competing for uptake with N, K, and Ca.
If you want to be a soil expert, check out this series of learning modules from U Montana http://landresources.montana.edu/NM/
If you want to be a soil expert, check out this series of learning modules from U Montana http://landresources.montana.edu/NM/