Identifying predictive biomarkers of patient outcomes from high-throughput microbiome data is of high interest, while existing computational methods do not satisfactorily account for complex survival endpoints, longitudinal samples, and taxa-specific sequencing biases. We present FLORAL (https://vdblab.github.io/FLORAL/), an open-source computational tool to perform scalable log-ratio lasso regression and microbial feature selection for continuous, binary, time-to-event, and competing risk outcomes, with compatibility of longitudinal microbiome data as time-dependent covariates. The proposed method adapts the augmented Lagrangian algorithm for a zero-sum constraint optimization problem while enabling a two-stage screening process for extended false-positive control. In extensive simulation and real-data analyses, FLORAL achieved consistently better false-positive control compared to other lasso-based approaches, and better sensitivity over popular differential abundance testing methods for datasets with smaller sample size. In a survival analysis in allogeneic hematopoietic-cell transplant, we further demonstrated considerable improvement by FLORAL in microbial feature selection by utilizing longitudinal microbiome data over only using baseline microbiome data.