"lalo" is "more so" "mas lalo" is "even more so" Si Jose ay mayaman, pero lalo na si Maria, at mas lalo na si Clara = Jose is rich, but more so is Maria, and even more so is Clara. "Ipinatawag ko kayo dito upang mas lalong makilala ng mundo ang ating kultura" = I called you here so that the world may learn about our culture even more so

It means more especially. Mas means more and lalo means especially or surpassing/greater degree.

For your example, I would translate it as "better/further"