It's about time Lux got some love.
I'd strongly support Chalice over Tear in any matchup. Lux's cooldowns are long so you can't spam anything to charge tear. Plus, because of that she benefits a lot from having the CDR. Chalice is made for her.
LeBlanc may be able to dodge skill shots, but Lux can be good against her because of her wave-clear. Shoving her in early will make the lane rough for LB; then it's just a matter of not over-extending when she can combo you.
I haven't really played the last few patches but Luden's Echo is a movement speed item, right? Going that before Deatchap is probably a good idea because, firstly, Deathcap is often cautioned against as a first-big AP item buy since its passive is a multiplier. The item's value is higher when you have more AP later in the game. Secondly, Lux benefits greatly from movement speed for kiting and positioning. In fact her base movement speed was one of the things they nerfed on her previously to bring her down from top-tier. Therefore, Grail > Luden should be an ideal path.