I cannot find record of the 1935 Baltimore Tigers in newspaper archives. That does not mean this photo isn't exactly what it indicates only that it may take a regional library with microfiche on site to track this team down. It may be easier to track individuals on the team like "Luke Hall" or "Herb Young" through genealogy records.

That season, the most popular black baseball team in town was the 1935 Baltimore Giants, but their lineup does not match any of the names: McCoy (CF), Patterson (3B), Shopp (SS), Vaughn (1B), Sanders (RF), Downey (C), Tyler (LF), Dyson (2B), Thompson (P), Day (P), Greene (2B), and Downes (P). 5-28-35 Hanover Evening Sun.

Too many African American baseball teams named the "Tigers" to narrow it down even by year. In 1935 alone there were black barnstormers; the Boston Colored Tigers, Cincinnati Tigers, Charleston Tigers, Elrod Tigers (NC), Dewey Tigers (IA), Kingsport Tigers (TX), Marietta Tigers (TX), and Claybrook Tigers (AR) to name only a few in a brief search. One team stands out as more likely than others, Washington DC's LeDroit Tigers, but I can't seem to locate them in 1935 (or after 1926 for that matter). I do not see Sam Lacy in the photo but there is a photo of him in a LeDroit uniform somewhere on the internet. Here's a brief article on Lacy: http://www.greatblackheroes.com/sports/sam-lacy/

Not exactly the definitive answer you were looking for, but do not be discouraged, this may take some time. Keep digging, it's a great pic!