The lottery ticket hypothesis (LTH) claims that a deep neural network (i.e., ground network) contains a number of subnetworks (i.e., winning tickets), each of which exhibiting identically accurate inference capability as that of the ground network. Federated learning (FL) has recently been applied in LotteryFL to discover such winning tickets in a distributed way, showing higher accuracy multi-task learning than Vanilla FL. Nonetheless, LotteryFL relies on unicast transmission on the downlink, and ignores mitigating stragglers, questioning scalability. Motivated by this, in this article we propose a personalized and communication-efficient federated lottery ticket learning algorithm, coined CELL, which exploits downlink broadcast for communication efficiency. Furthermore, it utilizes a novel user grouping method, thereby alternating between FL and lottery learning to mitigate stragglers. Numerical simulations validate that CELL achieves up to 3.6% higher personalized task classification accuracy with 4.3x smaller total communication cost until convergence under the CIFAR-10 dataset.