With the constant changes in NCAA DI volleyball coaches and rosters, there will be a bunch of scholarships awarded to high school Seniors this year. At USA Volleyball Nationals in Dallas last year, there were DI schools still scholarship recruiting graduated seniors for that fall's collegiate season.
Please note that NCAA DIII does not provide athletic scholarships, so while she would be able to play both sports (the lacrosse season is in the spring?), the cost of this opportunity would be borne by the family (or hopefully academic/merit/need base scholarships).
5'11" as a MB would be on the small side for DI and may limit her options to lower DI conferences, but her ability to touch a basketball rim would be a big plus. As a 5'11" OH, who jumps very high, she would be much more attractive to DI schools and could push into the mid-major category. OH's must have some semblance of ball control and this should be kept in mind when evaluating the recruiting opportunities.
The most troubling item in your email, was the coach saying that 'she could get her a DI scholarship' - As I have written online and Inside College Volleyball, the days of the high school coach 'getting' a player a scholarship are gone, unless the player is such a stud that the Starbucks drive thru person could 'get' a scholarship for a player.
I say this not out of disrespect for the coach, but rather the reality of thousands of 5'11" outside hitters who jump high - The Toyota Camrys of the volleyball recruiting world. The mistake that too many VolleyFamilies make is turning over the recruiting process to the high school or club coach and hoping for the best.
If your daughter wants to play collegiate volleyball on a scholarship, then the family has to commit to the recruiting process. College volleyball is more popular (better funded) than lacrosse, so the players will receive much larger scholarship awards. For DI, it is a Full Athletic Scholarship and with excellent support. For DII, it can easily package into a full scholarship by combining athletic, academic, merit and need based avenues. To garner these opportunities, the family has to be very proactive and engaged; waiting for it to be done by a coach or hoping that a college coach will see your VolleyPSA at a club event not effective.
In situations such as yours (good athlete, solid but not great height, talented player), I strongly recommend NCSA Athletic Recruiting. As I mentioned above, you must be proactive and manage the recruiting process. Because of NCSA's technology, resources and support, they are built for those athletes that need that extra boost to get seen and recruited. The NCSA Free Site is amazing with excellent resources for families, and their paid services are first rate. At the very least, get onto the Free Site to research schools, NCAA rules, watch webinars, etc.
In closing, you have got to make a decision - Either she goes all in for college volleyball or not. As club season is just around the corner, now is the time to put the plan of attack together!