Although the official record shows that there were no deaths on May 2, the figures could represent a lag or undercount due to weekend reporting.
As per the press release on the COVID-19 situation by the Los Angeles County Department of Public Health on May 2, 2021, the county recorded zero deaths, with 313 new COVID-19 cases. Although, it points that the "number of cases and deaths are likely to reflect reporting delays due to the weekend." Hence the claim is partly true.
Los Angeles records a cumulative of 1,233,772 cases and 23,915 deaths up to May 2. As of April 28, 7,862,893 vaccine doses have been administered.
According to the data, there is a reduction in transmission in Los Angeles. The press release on May 04 states, "Los Angeles County's adjusted case rate dropped from 2.7 new cases per 100,000 people to 1.9 new cases per 100,000. The evidence-based positive case rate fell from 1.2% to 0.9%, and in areas with fewer health resources, Los Angeles County's evidence-based positive case rate decreased from 1.4% to 1.0%."
On May 4, 2021, the county qualified for the least-restrictive yellow tier of the state economic-reopening blueprint due to declining COVID-19 cases. The adjusted case rate dropped from 1.9 to 1.6 new cases per 100,000 people. From May 6, a revised order permitting more activities and relaxations would be effective in the country.
The COVID-19 pandemic has given rise to a lot of potentially dangerous misinformation. For reliable advice on COVID-19 including symptoms, prevention and available treatment, please refer to the World Health Organisation or your national healthcare authority.