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.
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If you want to be a soil expert, check out this series of learning modules from U Montana http://landresources.montana.edu/NM/
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If you want to be a soil expert, check out this series of learning modules from U Montana http://landresources.montana.edu/NM/