Lake (pictured) claimed silver in the women’s 40-44 age category and was fifth overall in a time of 35 minutes and 37 seconds, which included the transition.
She completed the swim in 15.05 minutes and the run in 19.59 minutes.
Lake was only beaten by her Great Britain team-mate and world champion Tina Wilson, who took gold in a time of 34.09 minutes.
Great Britain actually claimed a one-two-three in that age category with Amy Pritchard taking bronze in 35.43.
Lake, who swims for Tavistock SC, managed to beat Katie Nimmo, who had won silver ahead of her at the World Championships in July.
“I’m over the moon,” said Lake. “The standard was extremely high. I beat the girl who beat me in the World Championships so I had to massively up my game to medal this time.”
Her Tavistock AC colleague Kula-Przezwanksi won gold in the women’s 55-59 category.
Kula-Przezwanksi, one of the oldest in her age group and a member of Caradon Swimming Club, clocked an impressive time of 40.45 minutes overall. She completed the swim in 15.49 minutes and the run in 24.19.
Another Tavistock athlete Louisa Shaw came 16th in the women’s 35-39 category.
Meanwhile, in the ETU European Cross Duathlon also held in Ibiza, Rockin Bikes’ Richard Long finished eighth in the men’s 25-29 age category and 33rd overall.
“I performed the best I could on the day but I’m disappointed,” said Long (pictured). “I underestimated the event so badly. It was great fun pulling on the GB colours and I’m excited to do it again in the future learning from my complacency from this one.
“A tiny consolation is that I was first Brit across the line.”