When Henry IV took the throne, he wasn’t exactly the natural successor to Richard II, although he certainly had a place on the list! I’m being a little facetious here; there wasn’t really a “list”, and a lot had to do with whether the crown was inherited by absolute primogeniture (where the sex of the heir is not relevant) or in tail male (where males only can inherit). This was not etched in stone during the high middle ages. In 1290 Edward I made a settlement permitting his daughters to succeed. Then Edward III made an entail only allowing the succession in the male line. Allegedly this entail was kept secret, because John of Gaunt, next in line, was very unpopular at the end of Edward III’s reign. Both kings’ original entails have been lost, possibly destroyed by a later monarch. After all, how long was an entail supposed to last? Forever? Or until it was superseded by another?
One thing is for sure: Richard II absolutely did not want Henry Bolingbroke to succeed him. As early as 1394, before his first expedition to Ireland, he appointed Edmund Langley, Duke of York as keeper of the realm. (York was the younger brother of Gaunt.) This overrode John of Gaunt’s request that the post go to Henry. Traditionally the keeper of the realm was heir presumptive, so this was a real slap in the face to Gaunt. All the way to the end of Richard’s reign, York was unofficially his choice of heir, and after him, Edward Rutland, the king’s cousin and favorite. If Richard ever made it official, this too was lost.
But this wasn’t the only complication. Gaunt’s older brother Lionel died in 1368 leaving only a daughter who married Edmund Mortimer, the 3rd Earl of March. They had a son, Roger, who many thought was the heir to the throne. Since Roger was descended from the daughter, according to Edward III’s entail he was disqualified. But few knew about the entail, and Richard had little interest in the Mortimers. Roger was killed in Ireland in 1398, leaving behind a young son.
So when Richard was usurped in 1399, Mortimer was too young to stand up for himself. Edward Rutland never made a fuss over the succession. This left Henry Bolingbroke, who took young Mortimer under his “protection”. Ironically, the Yorkists, who will resurface during the Wars of the Roses, are descended both from the Duke of York and the Mortimers, giving them a somewhat stronger claim than Lancaster. But that’s another story.