To answer your question rushing a lantern is only sometimes worthwhile. If youre top against someone who you need to build some lifesteal, armor, and ad against, I would definitely recommend it. However, Frozen Mallet is your proverbial "Bread and Butter". I would usually recommend boots1 into phage into merc/ninja. If you have lots of early game money it can be useful to build a lantern after your mallet too.
Also, I recommend Ghost+Ignite. Ghost+Ult is insane in team fights and ignite is better for battling than exhaust and has alterior uses. I usually stay away from warmogs on Olaf because it doesn't fit well for him as an early game item, and its not worth it to build late game.
Thank you for that question, I'll admit it was quite difficult to answer have a great day <@)