Jurgen Klopp revealed that the duo were both doubts in his pre-match press conference on Thursday, but they have since recovered from muscle and knee injuries respectively.
This relieves pressure on Klopp as he looks to name a strong starting lineup against an improving Palace side.
Teenager Joe Gomez had been expected to partner Lovren at Anfield, but this seems much less likely at this stage.
Henderson is yet to return to light training, and could miss the rest of the season, as with Bogdan, Ings and Mane, but Lallana is stepping up his recovery at Melwood.
The England midfielder is likely to rejoin the squad for their trip to Vicarage Road to take on Watford on May 1.
Two academy hopefuls joined the Reds first team on Thursday, with striker Rhian Brewster and midfielder Matty Virtue linking up with the more regular young faces.
Ovie Ejaria has also rejoined first-team training having recovered from a long-term ankle injury, though it is unlikely the 19-year-old will come into contention for Sunday.
The Brazilians will be particularly key to Liverpool securing a top-four finish this season, with five games left to play.
Given the fitness of his squad in the buildup to Sunday, Klopp could opt to make just one change to his starting lineup from the Hawthorns, with Matip likely to drop out.
The centre-back was pictured alongside Nathaniel Clyne at Melwood, however, suggesting a return to training was not far away.