They met with President Volodymr Zelensky, who has repeatedly called for allies to loosen limits on the use of Western-supplied weapons.
The US and UK have not given Ukraine permission to use long-range missiles against targets inside Russia for fear of escalation.
US President Joe Biden has said his administration is considering lifting the restrictions, but no decision has yet been made public.
Lammy said Iran providing Russia with ballistic missiles "clearly changes the debate" as they would allow Moscow's forces "to have further penetration into Ukraine".
Lammy said the UK would provide £600m ($780m) in aid to Ukraine to support the country's "humanitarian, energy and stabilisation needs".
Asked by reporters on Tuesday if the US would lift restrictions on Ukraine's use of long-range weapons, President Biden said his administration was "working that out now".
But Ukrainian leaders say they need the missiles to target air bases used by Russian warplanes to launch devastating glide bombs against Ukraine. »