A longing; especially for something that is forbiden.

'Lust of the flesh' would then be a longing or eager desire for the forbidden things of the flesh. (See Galatians 5:19-21)

This I say then, Walk in the Spirit, and ye shall not fulfil the lust of the flesh. For the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other: so that ye cannot do the things that ye would. But if ye be led of the Spirit, ye are not under the law.
Galatians 5:16-18