Ukrainian forces probably withdrew from Lysychansk on purpose, which is why the Russians captured the city on July 2.
This is stated in the morning summary of the Institute for the Study of War.
The Ukrainian military did not officially announce the withdrawal of troops, but also did not report about the defensive battles around Lysychansk. Russian forces are likely to establish control over the remaining territory of Luhansk Oblast in the coming days, and will most likely then strike Ukrainian positions in Siversk before returning to the offensive on Slovyansk and Bakhmut. The withdrawal of Ukrainian troops to Siversk will allow Ukrainian forces to reduce the risk of immediate encirclement.
Regarding other matters, the Ministry of Defense of the Russian Federation stated that on July 2, Chief of the General Staff Valery Gerasimov inspected the grouping of Russian troops in Ukraine. Although the Russian Ministry of Defense posted a slide show of images that allegedly prove that Gerasimov was recently in Ukraine, it is noteworthy that there were no video recordings of Gerasimovʼs inspection of Russian troops. Presumably, the Russians thus tried to refute reports that Gerasimov was removed from his post as part of a "purge" due to Russiaʼs failures in the war.