Due to numerous quotes available the reader can be quite confident (although not 100% confirmed) about which of Rhaegar's friends were with him when he "kidnapped" Lyanna. I thought it would be interesting to look into them as characters as well as their actions/whereabouts around this timeframe.

With the coming of the new year, the crown prince had taken to the road with half a dozen of his closest friends and confidants, on a journey that would ultimately lead him back to the riverlands. Not ten leagues from Harrenhal, Rhaegar fell upon Lyanna Stark of Winterfell, and carried her off, lighting a fire that would consume his house and kin and all those he loved—and half the realm besides.

Thoughts/Theories on Rhaeagar's 6 Friends Who Helped Him "Abduct" Lyanna

Background

The events surrounding the Tourney at Harrenhal are "well known". The details afterwards are a little more scant. We know (from before the Tourney even) that factions were growing especially a division between men loyal to Aerys and men loyal to Rhaegar (not even taking into account the STAB alliance).

Chief amongst the Mad King's supporters were three lords of his small council: Qarlton Chelsted, master of coin, Lucerys Velaryon, master of ships, and Symond Staunton, master of laws. The eunuch Varys, master of whisperers, and Wisdom Rossart, grand master of the Guild of Alchemists, also enjoyed the king's trust. Prince Rhaegar's support came from the younger men at court, including Lord Jon Connington, Ser Myles Mooton of Maidenpool, and Ser Richard Lonmouth. The Dornishmen who had come to court with the Princess Elia were in the prince's confidence as well, particularly Prince Lewyn Martell, Elia's uncle and a Sworn Brother of the Kingsguard. But the most formidable of all Rhaegar's friends and allies in King's Landing was surely Ser Arthur Dayne, the Sword of the Morning.

and:

"I make no such claim, ser. Myles Mooton was Prince Rhaegar's squire, and Richard Lonmouth after him. When they won their spurs, he knighted them himself, and they remained his close companions. Young Lord Connington was dear to the prince as well, but his oldest friend was Arthur Dayne." -ASOS, Daenerys I

From the above quotes I think we can look at what Rhaegar was doing after the Tourney of Harrenhal:

As cold winds hammered the city, King Aerys II turned to his pyromancers, charging them to drive the winter off with their magics. Huge green fires burned along the walls of the Red Keep for a moon's turn. Prince Rhaegar was not in the city to observe them, however. Nor could he be found in Dragonstone with Princess Elia and their young son, Aegon. With the coming of the new year, the crown prince had taken to the road with half a dozen of his closest friends and confidants, on a journey that would ultimately lead him back to the riverlands. Not ten leagues from Harrenhal, Rhaegar fell upon Lyanna Stark of Winterfell, and carried her off, lighting a fire that would consume his house and kin and all those he loved—and half the realm besides.

and assume that Rhaegar's six friends were:

• Oswell Whent
• Lewyn Martell
• Arthur Dayne
• Jon Connington
• Myles Mooton
• Richard Lonmouth

Rhaegar's Friends Actions/Whereabouts

Oswell Whent

The Tourney was announced after a visit to Harrenhal by Oswell (likely with an offer of financial backing from Rhaegar).

Oswell doesn't appear again until the Tower of Joy where he is killed by Ned + Co.

Lewyn Martell

Lewyn attended the tourney at Harrenhal, but Aerys kept Elia during Robert's rebellion to ensure Lewyn/Dorne's loyalty.

He was slain on the Trident by Lyn Corbray.

Arthur Dayne

Arthur attended the tourney at Harrenhal, and like Oswell (who are both confirmed by the app to have been with Rhaegar during the kidnapping) he doesn't appear again until the Tower of Joy scene.

If interested: The Dayne Name

Jon Connington

After the Tourney at Harrenhal, JonCon later became hand after Owen Merryweather's dismissal as Aerys wanted a younger man to match Robert's energy. After his defeat in the Battle of the Bells, he was stripped of his office/titles and fled across the Narrow Sea.

Richard Lonmouth

Confirmed to have been at the Tourney at Harrenhal, it should be noted that not only was Lonmouth a close friend of Rhaegar's, but he also spent some time with Robert there:

The storm lord drank down the knight of skulls and kisses in a wine-cup war. -ASOS, Bran II

It is unknown what Lonmouth did during Robert's Rebellion and he is the only person on this list with an unknown fate. It is theorized quite heavily that Richard = Lem Lemoncloak and if that is the case, the BWB and Jaime Lannister's showdown in TWOW should be even more interesting due to the fact that Richard Lonmouth and Jaime likely do not get along:

Nor did His Grace agree to appoint Lord Tywin's son Jaime as squire to Prince Rhaegar; that honor he granted instead to the sons of several of his own favorites, men known to be no friends of House Lannister or the Hand. TWOIAF, The Targaryen Kings: Aerys II

Myles Mooton

Myles is the only character on this list that is unconfirmed to have been at the Tourney at Harrenhal. Similar to Richard Lonmouth it is possible he doesn't get along with Jaime.

Myles was killed in the Battle of the Bells by Robert Baratheon.

It should be noted again that Arthur Dayne and Oswell Whent are confirmed by the semi-canon app to have been with Rhaeagar.

TLDR: Just some thoughts to spur discussion on Rhaegar's Six Companions who "abducted" Lyanna and what happened to them.