Your overall build sounds wrong. Taliyah wants to start Luden’s Echo, Sorcerer’s Shoes, and Morellonomicon. Then she wants to scale her damage with Liandry’s Torment and Void Staff, choosing Zhonya’s Hourglass to defend against comps with reliable backline access and Rylai’s Crystal Scepter to defend against ones without.
Taliyah isn’t a Rod-and-Tear battlemage who wants to wade into the fray and sling spells like Vladimir, Swain, or Cassiopeia do. She’s a roaming, kiting pick mage who wants to ride her rock and find chances to blow up squishies and burn down everything else.
Hence, she needs the 20% CDR from a Lost Chapter item, with Luden’s Echo being the best choice for its quick spike, extra waveclear and poke, and longer and wider reach due to the bolt travel distance. She also has huge base damage, which the flat Magic Penetration from Sorcerer’s Shoes and Morellonomicon helps get onto targets.
However, this build leaves her squishy, and since she does deal DPS, opting into battle mage items afterward delivers sustained damage and anti-burst survivability. Hence the choice of Liandry’s Torment. Her AP scalings are so low, however, that Deathcap is good only for snowballing, leaving Void Staff as her damage-amp item. This choice also synergizes with her high base damages.
Rylai’s Crystal Scepter continues the AP-Health-DPS approach, but it can be taken only against comps that lack reliable backline access. Against those comps, instead take Zhonya’s Hourglass for armor, CDR, and the active.
Try this build out, play around your squishy-ness, and look for repeated Q burns on the frontline and devastating W-E combos on the backline.