How is the relevant question actually worded on the ESTA form? If it only asks about 'convictions' you're in the clear as far as 'lying' is concerned, since a caution is NOT a conviction.
(Before someone else points it out, I know that accepting a caution is acknowledging carrying out an offence which, if it relates to 'moral turpitude', still carries an automatic ban on admission to the USA under the US Immigration and Nationality Act. My post relates purely to whether inaccurate information was provided in the ESTA application)