The correct phrase is "lie in bed" when referring to reclining or resting in bed.
"Lie" is an intransitive verb meaning to recline or rest on a surface (no direct object).
- Present tense: I lie in bed
- Past tense: I lay in bed
- Past participle: I have lain in bed
"Lay" is a transitive verb meaning to put or place something down (requires a direct object).
- Present tense: I lay the book on the table
- Past tense: I laid the book on the table
- Past participle: I have laid the book on the table