E-Science Grid is designed to cope with computation-intensive tasks and to manage a huge volume of science data efficiently. However, certain tasks may involve more than one grid can offer in computation capability or incur a long wait time on other tasks. Resource sharing among Grids can solve this problem with proper processing-integrity check via audit. Due to their computing-intensive nature, the processing time of e-Science tasks tends to be long. This potential long wait before an audit failure encourages earlier audit mechanism during execution in order both to prevent resource waste and to detect any problem fast. In this paper, we propose a Light-weight, Adaptive and Reliable Audit, LARA, of processing Integrity for e-Science applications. With the LARA scheme. researchers can verify their processing earlier and fast.