batting or pitching with runners in scoring positon is a bizarre stat to try to read.
The real thing that you might look for is from a pitching perspective, does the pitcher panic and turn to mush just because they have someone in scoring position, thus making everyone bat better against them cause they become more errattic.
For batters it can be a similar thing, do they press more, thus swinging at more "bad" pitches because they are over anxious to drive in that run, that they are afraid to "waste" their chances. Or they could be the opposite of the spectrum and go too timid waiting for the perfect pitch not wanting to screw it up. Either extreme is bad, and while there are some hitters who simply hit better in the in those situations, typically it will be those who have a normally "good batting eye" thus Berkman is very good at this.
So the fact that Lee bats the same (relatively) with men on as his does any other time, then we can probably conclude he is just very consistent (which is still good to have) but is not particularly selective anytime (re-enforced by his average walk totals).
So I think he is a good hitter, who is at best a LF, at worst a DH type. Given the lack of good hitters on this team (from an RBI perspective) he would be a good addition. This does potentially block Pence, but then Scott is 28 and just now breaking in to the majors. He could either be a late-bloomer, or this is his career year and it is all down hill from here. Having Pence in your back-pocket is a nice thing to have to test that out at the start of next year.
So I expect Lee to be the #1 FA target this offseason, the real question then becomes, who else will they go after? Don't count on Soriano though he wants more lime-light than Houston can provide. Look for him to end up in NY, LA or Chicago. With Chicago being a last option, IMO.