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Apart from bedrock problems, of course you can construct a waterproof basement: you can construct a pool that is waterproof and does not let water out: why not a basement that does not let water in?
In construction, the question is almost NEVER "can we" but "how much would it cost?" You can do almost anything with an unlimited budget: you can erect a giant, up-side down pyramid if you want to.
The cost will depend quite a bit upon the depth of the water table at your location. If you live on a 300-foot bluff overlooking the lake, you probably will not have problems because the water table is well below you. If your land is entirely along the shoreline with no grade, it will probably cost more.