Objection 1. It seems that lust is not a capital vice. For lust is apparently the same as "uncleanness," according to a gloss on Ephesians 5:3 (Cf. 2 Corinthians 12:21). But uncleanness is a daughter of gluttony, according to Gregory (Moral. xxxi, 45). Therefore lust is not a capital vice.
Objection 2. Further, Isidore says (De Summo Bono ii, 39) that "as pride of mind leads to the depravity of lust, so does humility of mind safeguard the chastity of the flesh." Now it is seemingly contrary to the nature of a capital vice to arise from another vice. Therefore lust is not a capital vice.
Objection 3. Further, lust is caused by despair, according to Ephesians 4:19, "Who despairing, have given themselves up to lasciviousness." But despair is not a capital vice; indeed, it is accounted a daughter of sloth, as stated above (35, 4, ad 2). Much less, therefore, is lust a capital vice.
On the contrary, Gregory (Moral. xxxi, 45) places lust among the capital vices.
I answer that, As stated above (148, 5; I-II, 84, 3,4), a capital vice is one that has a very desirable end, so that through desire for that end, a man proceeds to commit many sins, all of which are said to arise from that vice as from a principal vice. Now the end of lust is venereal pleasure, which is very great. Wherefore this pleasure is very desirable as regards the sensitive appetite, both on account of the intensity of the pleasure, and because such like concupiscence is connatural to man. Therefore it is evident that lust is a capital vice.
Reply to Objection 1. As stated above (Question 148, Article 6), according to some, the uncleanness which is reckoned a daughter of gluttony is a certain uncleanness of the body, and thus the objection is not to the point. If, however, it denote the uncleanness of lust, we must reply that it is caused by gluttony materially--in so far as gluttony provides the bodily matter of lust--and not under the aspect of final cause, in which respect chiefly the capital vices are said to be the cause of others.
Reply to Objection 2. As stated above (132, 4, ad 1), when we were treating of vainglory, pride is accounted the common mother of all sins, so that even the capital vices originate therefrom.
Reply to Objection 3. Certain persons refrain from lustful pleasures chiefly through hope of the glory to come, which hope is removed by despair, so that the latter is a cause of lust, as removing an obstacle thereto, not as its direct cause; whereas this is seemingly necessary for a capital vice.
Source: Summa Theologica (New Advent)