Lilith Lady of Lament special summoned by Tour Guide from the Underworld
Yes, Lillith's Effect Can Still Be Activated.

Tour Guide From the Underworld's effect states that the effects of the Special Summoned Monster are negated - not that they may not be activated. The distinction is important, because simply negating the effects of a card does not disallow attempts to activate those effects.

Applying the concept in the opposite direction, consider Majesty's Fiend, which simply says:


  Monster effects cannot be activated.


Given that continuous monster effects are not impacted by effects like that of Majesty's Fiend, we can clearly see a separation. In conclusion, unless the card specifically says "cannot be activated," or some rearrangement thereof, you can still attempt to activate the effect - provided of course that you can pay activation cost.