Does anyone else end up finding the lamp?

No

Not long after Izuku buried the lamp All Might arrived & they resumed cleaning the beach. He couldn't explain it, but Izuku kept sneaking glances back to where he had hidden the lamp. Almost like he was making sure no one found it.

He needn't have worried, he & All Might were the only ones on the beach for hours. Except for a couple that had come to dump their trash, ignoring the large dumpster he had sitting in the parking lot in full view. He actually confronted them, complaining about how they blatantly ignored the dumpster & was making his work all the harder.

The couple looked embarrassed, before apologizing & throwing their trash in the dumpster. Except for that one interaction, Izuku continued his task uninterrupted. Although his thoughts kept staying back to Momo. He mentally blushed whenever he remembered how her naked body looked.