Mackenzie Martin and Taine Basham are the other back-row options, with Taulupe Faletau and Jac Morgan missing through long-term injuries.
Prop Brown started the game against Scotland but was forced off at half-time because of a shoulder injury and replaced by Assiratti. Uncapped Bath prop Griffin is the other option in the squad.
Harlequins prop Lewis, 28, has played 54 internationals for Wales. The former Cardiff man was one of three tight-head props selected for the 2023 World Cup, alongside France-based Henry Thomas and Tomas Francis, who were not included in the original Six Nations squad.
Fly-half Sam Costelow is a doubt to face England, having being forced off the field in the first half against Scotland.
Head coach Warren Gatland afterwards confirmed he had failed a head injury assessment (HIA) during the game.
Wales have revealed since the issue was a neck problem rather than a concussion.
“The good news is it wasn’t a concussion, but he’s being assessed for a neural issue on his neck,” said Wales attack coach Alex King.
“So, it’s a positive thing it wasn’t a concussion.
“He’s up for selection, but it’s a question whether he gets through his medical protocols.”
Costelow was replaced by Ioan Lloyd who is in contention for a first Wales fly-half start at Twickenham.
Centre George North missed the defeat against Scotland with Owen Watkin partnering Nick Tompkins in midfield.
King says he has his “fingers crossed” when asked whether North would be fit to face England.
“He’s training well,” said King.
“The squad is getting announced later this week. It’s good to have him back.
“He had a great World Cup and his relationship with Nick (Tompkins) in that midfield was one of the highlights of that campaign.
“It’s frustrating he wasn’t around last week, but I thought Owen had a good game and it’s good to have some competition for places.”
Lock Will Rowlands is also back in training after missing the Scotland game following the birth of his baby.