The body of Daniel Williams, was found in Whiteknights Lake at the University of Reading campus on Tuesday.
Mr Williams went missing on 31 January following a night out at the university, prompting a six-day search.
The university said it would review any concerns raised, along with outcomes from the police investigation.
The death of the student, from Sutton, London, was being treated as unexplained and was not believed to be suspicious, Thames Valley Police has said.
The petition, started by student Ellie Slaney called for the university to install lights around the lake, following the “recent awful incident”.
On the change.org page, Ms Slaney says: “We need lights round our lake.
“Taking into account the high frequency of people who walk around Reading’s Whiteknights Campus lake at all hours of the day and especially after the recent awful incident, I think we should start urging the university to realise that proper lighting around the lake walkways is a necessity.”
Many of the thousands who have signed the petition have commented saying they are signing “for Daniel”.
A university spokesperson said “Speculation around the circumstances of the tragic situation on campus is disrespectful.”
The acting vice-chancellor has invited the petitioners to meet him to discuss their concerns further, they added.
Mr Williams’ family described him as “a happy, normal 19-year-old enjoying university life” and said they had “no concern at all” about him before he went missing.
Lead investigator Supt Jim Weems described the disappearance as “completely out of character”.
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