Is it true that the second ionization energy of elements is always greter than the first ionization energy?

Not necessarily.

For Alkali Earth metals like Be, Mg, Ca, Sr, Ba, the second ionization potential is lesser than the first IE as they attain a Alkali metal valece configuration after the first Ionization.

yes  for example-

take Na (sodium) when one outer electron is removed  I.E 1

NOW IT ATTAIN configuration of neon hence removal of electron require high energy then I.E1