Lewandowski found the net in the 14th and 17th minutes in Bilbao to finish the season with 27 goals, four fewer than Frenchman Mbappe, who scored twice in Real Madrid's 2-0 win against Real Sociedad on Saturday.
Poland international Lewandowski hadn't scored since April 9 in a Champions League match against Borussia Dortmund, and his last goal in La Liga had been in March against Girona. Dani Olmo got the third at San Mames in added time.
Barcelona finished with a goal-difference of plus 63 after scoring 102 times and conceding 39. They won 28 matches, drew four and lost six, ending with 88 points, four points more than second-placed Madrid and 12 more than third-placed Atletico.
Athletic had already secured a fourth-placed finish to secure a Champions League spot for the first time in a decade.
Lewandowski reached 101 goals in total across all competitions in his three seasons with Barca. He had 42 this year after scoring 26 last season and 33 in his debut campaign.
"We had it under control," the 36-year-old said.
"This season was almost perfect. We have to enjoy this moment."
Despite their disappointing Champions League semi-final elimination by Inter Milan earlier this month, Barcelona coach Hansi Flick still had praise for his team.
"We wanted to finish like we started it, like we performed during the season, and they did a great job," the German said.
Elsewhere on Sunday, Atletico finished their season with a 4-0 win at Girona.
Norwegian striker Alexander Sorloth netted a hat-trick to end the campaign with 20 goals, fourth in the league's scoring list, and fifth-placed Villarreal beat 17th-placed Sevilla 4-2 with a pair of goals by Pape Gueye.
