You'll find that a good cutting lubricant will do more to help you along in drilling the holes than multiple new drill bits without lubricant. 

If all your bits are dull, which they might be if you haven't been using them with lubricant, get one new bit for the job.  One decent bit and a good hand drill will do the job and if you don't think cutting oil has any value -- use it on all but the last hole, you'll think you're using a totally different bit.

Don't try skipping the lubricant on the first hole as you'll only get your bit hot and get tired of pushing on your drill.  And don't be afraid to use the lubricant liberally, as the lubed drill bit removes material (those curly strands of metal) you'll need to constantly be re-lubricating the cutting edges to keep them cool.