It depends more on workflow than file format. Lightroom is not inherently overkill for JPEG shooters: its strongest benefits are often organization, rating, searching, export, printing, and having everything integrated in one place. If those features would save you time, it can be worthwhile even if you only do light edits or mostly crop.

That said, if you’re happy with Picasa’s speed and simplicity and only make basic adjustments, Lightroom may feel like more complexity than benefit. Several users find Picasa easier for straightforward folder-based use, especially if you want minimal learning curve and don’t need a database-driven catalog.

A practical middle ground is to keep Picasa for organizing and basic edits, and add a small external editor for the occasional image that needs more work. If you increasingly want better cataloging, ratings, export control, or occasional RAW processing, Lightroom becomes more compelling.

So: for a mostly JPEG, minimal-edit workflow, Lightroom can be useful but is not a must-have. If Picasa already fits your needs, it’s reasonable to stay with it until your organizational or editing needs outgrow it.