Bash syntax error when “else” follows an empty “then” clause

It seems that you want to do a no-op if the file is open so you should add a :, which is a null command in bash:

if lsof "$filename" > /dev/null
then
  # file is open
  :
else
  echo "deleting $filename"
  rm "$filename"
fi

If you don't use :, bash can not parse you code, and will show error like bash: syntax error near unexpected token 'else'.

Another alternative: reverse your logic.

if ! lsof "$filename" >/dev/null;then
    echo "deleting $filename"
    rm "$filename"
fi

TL;DR

None of the other answers actually addresses your original question of why the command gives a syntax error. This is caused by a missing command between then and else.

A Missing Command

Your original code looks like this:

if lsof "$filename" > /dev/null
then
  # file is open
else
  echo "deleting $filename"
  rm "$filename"
fi

The problem is that you have a comment between then and else, but the comment isn't treated as a command. In short, you could rewrite the problem you have (structurally speaking) as follows:

$ if true; then else echo; fi
bash: syntax error near unexpected token `else'

Fix Your Syntax with a Bourne Builtin

You can fix this problem by placing actual commands before else, but a comment by itself won't do. The if-then section can't be empty; if you want a placeholder, you can use the colon builtin. For example:

$ if true; then :; else echo; fi

Simply placing : into the section between then and else will fix the syntax error you are experiencing.