Ms Carleton owned the Mag.Pi clothing store in Cedar Glen, which is located in the San Bernardino mountains.
Hollywood actress Bridget Everett said vandals had attacked the rainbow flag outside the store before.
A local LGBT group also paid tribute to a friend and supporter.
“Lauri did not identify as LGBTQ+, but spent her time helping & advocating for everyone in the community,” it wrote on Instagram.
According to the US Department of Justice, 15.6 per cent of hate crimes in 2021, the latest year for which figures are available, were attributed to sexual orientation.
In April, an Ohio man was charged with using Molotov cocktails to burn down a church which was planning to hold drag shows.
In the same month, the Department of Justice reported that a Maryland man had been charged with a hate crime after leaving a threatening voicemail on the answerphone of an LGBTQ group.
A report from the Anti-Defamation League and the LGBTQ+ organisation GLAAD shows there have been more than 350 incidents of harassment, vandalism or assault from June 2022 to April 2023.