The Rojillos return from Fuerteventura with a share of the points after playing the majority of the match with 10 men.
Centre back Chucky Pierce was dismissed with a straight red card in the 37th minute for a high challenge.
Despite playing with a man less Lanzarote took the lead from a header from Alex Cruz three minutes into the second half.
The Fuerteventura side levelled in the 56th minute from a well worked free kick and seven minutes later the home side went 2-1 up as the Rojillos defence looked tired.
In the 76th minute the ever alert striker Di Renzo pounced on a loose ball and drilled the ball low and inside the right hand post from the edge of the area to make the score 2-2.
Lanzarote must be content with their point after playing in the heat for well over an hour with a man less. With two matches played the Rojillos have four points and are in fourth spot.
Next Sunday at 12 noon Lanzarote are at home and face local side San Bartolomé CF for their first ever meeting in Spain’s Tercera Division.
0-1 min 48 Alex Cruz
1-1 min 57 Eslava
2-1 min 62 Kai
2-2 min 77 Gonzalo Di Renzo