Is there a USBC rule that states that the team captains can not draw numbers out of a hat each week to determine which lanes they bowl on?  The computer would determine who bowled who but just draw numbers to decide which lanes so that there could be no tampering with the lanes.

Sometimes, as I mentioned in your "other" post, it becomes necessary to do this and a rule can be incorporated to accomplish this.  Typically, the first place team draws the first number (even or odd depending on which side they are scheduled), and all others proceed to the right as if the number drawn were the first pair. 

Example:  Your league bowls on 1-20.  The first place team captain (whichever team is listed on the top of the sheet in the event of a tie) draws lane 13.  Their opponents go to 14, then the next pair (which would have been on "3-4" would be on "15-16", then proceed to the right. 

I can see some drawbacks to drawing numbers to do lane assignments. One is getting the scorers set up since the center won't be able to have the info up on the screens in advance like most do. Another is having a representative of every team at the center early enough to draw the numbers to get things started. I've seen practice start with several sets of lanes not having any bowlers there yet. I do see where doing this can be beneficial though, such as when the lane man or proprierter bowls in the league and can possibly set up their lanes to their advantage, or screw up the lanes of teams that are ahead or close to them in the standings.

cpmichican:

I can see some drawbacks to drawing numbers to do lane assignments. One is getting the scorers set up since the center won't be able to have the info up on the screens in advance like most do. Another is having a representative of every team at the center early enough to draw the numbers to get things started. I've seen practice start with several sets of lanes not having any bowlers there yet. I do see where doing this can be beneficial though, such as when the lane man or proprierter bowls in the league and can possibly set up their lanes to their advantage, or screw up the lanes of teams that are ahead or close to them in the standings.

cpmichican:

Another thing to keep in mind is, at least in my experience, the leagues in question were match point leagues, so the lineups were not so etched in stone that they needed to be in place when the bowlers arrived.  Typically, the left lane posts its lineup first, then the right lane counters.  Granted, some teams maintain their lineup no matter who they bowl. 

Secondly, only the first place team "draws"; the rest follow along with that week's schedule based on the draw.