This paper addresses the task of (complex) conversational question answering over a knowledge graph. For this task, we propose LASAGNE (muLti-task semAntic parSing with trAnsformer and Graph atteNtion nEworks). It is the first approach, which employs a transformer architecture extended with Graph Attention Networks for multi-task neural semantic parsing. LASAGNE uses a transformer model for generating the base logical forms, while the Graph Attention model is used to exploit correlations between (entity) types and predicates to produce node representations. LASAGNE also includes a novel entity recognition module which detects, links, and ranks all relevant entities in the question context. We evaluate LASAGNE on a standard dataset for complex sequential question answering, on which it outperforms existing baselines averaged on all question types. Specifically, we show that LASAGNE improves the F1-score on eight out of ten question types; in some cases, the increase is more than 20% compared to state of the art (SotA).