If memory serves me right, when first envisioned, Lake Elizabeth was supposed to be an all recreational city park, with swimming, biking, fishing, etc.
As for the fishing part, the lake was stocked with trout on a regular basis, but only for a time. I believe the stocking started in the '70's, possibly late '60's, and ended sometime in the early '80's. I've never gotten a factual reason why the stocking program ended.
We grew up in Mission San Jose, and as for bass, we used to hike up to the ponds where Ohlone College now sits. They had some big bass in those ponds back then.