Do Lutherans believe that the sacraments are necessary for salvation (similar to Catholics), and if so, how do they reconcile this with Sola Fide? During my internet adventures browsing theological articles and blogs, I somehow picked up the idea that in a similar way to Catholics, Lutherans believe in baptismal regeneration and that baptism is, therefore, necessary for salvation.

I also picked up the idea that Lutherans have a robust "high" sacramental theology, similar to Catholics. However, perusing the Wikipedia article on "Lutheran Sacraments" reveals that Lutherans only believe in 3 sacraments, not 7.

I'm wondering, does Lutheranism believe that their sacraments are necessary for salvation (Baptism, Eucharist, Penance)? And if so, how do they reconcile that with the classic Protestant "Salvation by Faith alone" doctrine?
First, a Lutheran is not likely to recognize the phrase "salvation by faith". The usual construct Lutherans use is "justification by faith". For Lutherans, there is a distinction between the two. Salvation was assured by Jesus' death and resurrection. Justification assures believers that they are made worthy of the salvation secured for them by Jesus salvific act. The essential vehicle for communicating that assurance, for Lutherans, is the means of grace, the Word and the sacraments. So Lutherans do see the sacraments as essential, though not for salvation in the sense that the poster of the question seems to think.