Speaking as a re-enactor & lutenist (until the bloody thing broke... :( ), I doubt you strike a lute in any meaningful sense of the English. It might refer to rapping on the soundboard (most likely with the knuckles) in a similar fashion to some classical guitar pieces, but I can't find any reference to it in a brief skim of my immediately available resources.

Important questions: what type of lute, & what style of music are we talking about? Lute can be broadly (though not precisely) split into Renaissance & Baroque. Bach is quite different from Newsidler or Dowland (though still no rapping)! Also, as time went on, the lute tended to acquire more diapasons (open bass strings). Within Renaissance period, & I quote from A Tutor for Renaissance Lute by Diana Poulton, my main (& an excellent) resource:

As early as 1511 a seventh course was mentioned but no music from that date includes its use. By 1585 eight courses are shown... however, the greater part of the lute repertoire was still being written for a six course instrument. ...a tenth course... ...was the limit of the true Renaissance instrument. {& this occurs only into the 17thC}

I can't (on a skim) find any reference to any "striking" within the Poulton book. However, I also possess a large (A4) format booklet written by Andrew Lawrence-King, a noted harpist, entitled "Der Harpffenschlaeger", subtitled 'An introduction to "Authentic" technique for Early Harps', written in 1987/88, which is intended for pre-classical harps. It is based on both his personal experience & also "a broad base of hard information from reliable pre-classical sources". The author further notes that it works... better than modern technique in fulfilling the demands of stylistic performance of early music.

Early in the booklet he states The Germans used to call harpists "Hapffenschlaeger" - harp-beaters, and you should notice the difference between "striking" the strings, & the modern idea of plucking. If you put your finger behind the string and pull it, you are plucking. Instead, you should put your finger on the string, so that the finger-stroke is an action of releasing the string, not of pulling or plucking it. You can easily check that you are "striking" correctly, by pushing on the strings from your starting position. You should find that you can push the string at right angles before releasing the sound; if you've put your fingers past the string (as distinct from on it), you'll only be able to pull.

It should be further noted that Poulton makes the point that the lute, unlike the classical guitar is not played with the nails, nor is the correct hand position perpendicular to the strings.

The {Right Hand} finger nails must be short & must not touch the courses in playing. Except for one Italian teacher... and even he only advocates that the nail should be gently rounded to coincide with the tip of the finger... The long nails of the present day guitar player will prodcue an entirely unauthentic sound.

To bring the hand to the correct position the forearm should touch the upper edge of the lute just about level with the bridge. The hand is held obliquely across the strings continuing the line of the arm and, in the technique now being described, not at a right angle across the strings. The little finger is laid on the soundboard. This is a point of great importance and is mentioned in every book of instruction in which the right-hand technique is described.

I could add a few more minor technical points, but I hope this answers your question adequately. And with references! ;)