Answer: You can cut the tips off, but they will not grow back. There are several reasons why this might be happening. Dracaena tends to be sensitive to salts in the soil such as from fertilizer and to chemicals in the water such as chlorine and can show tip damage as a result of these. I would suggest you water with rain water or bottled water (drinking water, not distilled water) and if you can, remove the fertilizer spikes.
Since these plants grow very slowly they do not need a large amount of fertilizer. You might use a water soluble fertilizer at a very weak dilution from spring to fall, and leach the plant every six months. To do that, water heavily several times in succession to rinse excess salts out of the soil.
There is another possibility since it is lower leaves, and that is that it is naturally going to lose some of the lower leaves as the new growth comes along. The dimmer the light, the less foliage it will be able to carry.
I hope this helps you troubleshoot.
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