Clear EA? in code? I thought EA is accessed by hardware only.
Wrong!!!
EA -- Enable All Interrupts.
This bit is MSB D7 in IE [ Interrupt Enable register ].

When you clear this bit all the interrupts are disabled regardless of their individual bit status in IE. Erik is PUSHing this register on stack to save its content then he is disabling the interrupts by clearing EA then lcd operatrion is performed and when that is done IE is POPed back so as to restore the IE. and thus turning on the interrupts.
push IE
clr EA
setb ... enable LCD write
clr ... disable LCD write
pop IE