Having taken the decision to freeze two-time Premier League title winner Diego Costa out of the fold, Antonio Conte was forced into the transfer market over the summer.
Morata was acquired from Real Madrid, and the Spain international has settled quickly at Stamford Bridge to net nine times in 17 appearances.
Chelsea are, however, lacking depth in the striking department and Lampard believes that will force them to spend again when the next window opens, before then addressing their midfield needs in the summer of 2018.
The former Blues star told BT Sport: “I think they need to add [in January].
“If you’re looking at Morata there, Michy Batshuayi has come in and had moments where he’s scored but seemingly Conte doesn’t trust him.
“Then you have to play [Eden] Hazard there and change a lot of things. So I think maybe a backup striker.
“I think they are going to have to strengthen in midfield at some point but that may be next year.
“But I think you have to keep strengthening because everybody else is.
“Manchester City are, Manchester United are, so to stay in the game you have to keep strengthening.”
As well as landing Morata over the summer, Chelsea also brought in Antonio Rudiger, Willy Caballero, Tiemoue Bakyaoko, Danny Drinkwater and Davide Zappacosta.
The reigning Premier League champions have, however, slipped nine points off the pace in the 2017-18 title race and may need to bolster their ranks further in January if they are to remain in contention to defend their English top-flight crown.