Gerek is a Turkish word and lazım is a word that derived from Arabic. Gerek is both noun and adjective but lazım is only an adjective. There is no difference between their meanings, but gerek is a Turkish noun so you can decline it like; gerekli, gereksiz, gereği...etc.

Yumicik, iyi aksamlar! bence ayni.. kitabimda oyle yaziyordu

I think lazim is more like I have to and gerek is more I need to or there is a need for me to .. Don't know if it was any help but :)

Her iki kelimede aynı kapıya çıkar. Bu kelimelerin anlamca farklı kullanıldığı yerler de vardır. Ancak burada anlamca ve kullanımca aynı olan durumdan bahsedeceğim. Örnekler; Ders çalışman gerek. Ders çalışman lazım. You can think of these as an equivalent of the usage 'need to' or 'should'. So all roads lead to Rome.

evet ayni :)