Open a terminal and create a file .lesskey, in your home folder and append the following to it:

#env

LESSHISTSIZE=0

If you already have the file .lesshst in your home folder, then delete it and type the command

lesskey

You shouldn't get any errors here. This will not store any history of less from now on, until you change the .lesskey file.

From the man page of less:

ENVIRONMENT VARIABLES

   Environment variables may be specified either in the system environment

   as usual, or in a lesskey  (1)  file.   If  environment  variables  are

   defined  in  more  than one place, variables defined in a local lesskey

   file take precedence over variables defined in the system  environment,

   which take precedence over variables defined in the system-wide lesskey

   file.

LESSHISTSIZE

          The maximum number of commands to save in the history file.  The

          default is 100.

EDIT:

From the comments, I found a better way to prevent having a history file for less.

In the .lesskey file in the home folder, append this:

LESSHISTFILE=-

or

LESSHISTFILE=/dev/null

If you put this in your ~/.bashrc file, this will work, but will have a lower precedence if you have other values in your .lesskey file for the same variables.

You may want to have a look at this:

• How to make less more friendly