The recommendation to stop eating lemon and limes to prevent tooth decay is likely due to their acid content.
The primary nutritional benefits of citrus fruits are mainly vitamin C (ascorbic acid), though many other useful nutrients are also provided. Luckily, it appears that according to research the bio-availability of "artificial" vitamin C is not markedly reduced, and so supplements can be used.
There are other nutrients that fruits, though not only citrus, provides that may be unhealthy to cut completely out of your diet. "Phytochemicals" are a collection of plant-based chemicals that may have a multitude of benefits to health, but are not standard vitamins. Dietary fiber is also an important component of your diet that can often be provided by fruits, citrus or otherwise.
In summary, taking supplements of at least vitamin C is shown to be able to replace real citrus fruit intake for that nutrient, but there may be other nutrients that you should introduce through other foods (legumes and animal proteins are a good source of folate, as well as fortified grains) or through another supplement. There are also several low acid fruits that may be helpful while reducing tooth decay, assuming you brush after to reduce sugar left for mouth bacteria.