Lawrence, who has recently been restored to the first team having been transfer-listed earlier this season, suffered a hamstring injury at Scunthorpe last weekend and missed Tuesday night's defeat by Swansea.
And fellow centre-half Davis pulled out in the morning of the Swans game complaining of a sore groin.
Boss Neil Warnock's defensive headache is compounded by the fact young left-back Lee Hills, who came in against Swansea, is cup-tied.
Winger Kieron Cadogan and striker Stern John are also ineligible having played in the competition while on loan elsewhere this season.
