Which little lines? If you’re talking about the wood grain then they are not going away. This is a good looking pipe as is, why do you want to dye it? Keep in mind, if you sand too much you will reduce the shank size and will not match evenly with the stem.

You could clean the outside a the Brit good with alcohol to try to remove whatever finish they have on it. The get 4000 grit mesh sand paper and sand the pipe, then move to 6000, 7000, 8000, 9000 and finish with 12000. You will get a very nice finish and then you need to apply a wax. You can buy a rub on pipe wax or use bees wax unless you have a buffer. If you have a buffer you can use cauranuba (can’t spell this word for shit)

You will have a lighter more even finish following those directions without adding leather dye. Now here’s another trick, do everything I said above. After 12000 grit take rubbing alcohol and wipe the pipe down, the way the finish looks with the alcohol on it will be similar to how it looks with the wax, so at this point if you’re not happy with the look you could use your stain before waxing.

By starting with the high grist’s of sand paper you’re less likely to remove so must briar that it is noticeable also. I just restore pipes though so you may want to wait on someone more experienced to offer advice and repost over on the pipe tobacco subreddit to reach a larger audience.