In a word: yes!
But we have to work a bit harder, and make sure to get sufficient recovery (which is more than what we could get by on when we were younger).
As for 'not getting a lot of protein,' if you are eating a well-balanced veg diet, you probably are getting enough protein (and more). But if you are concerned about it, you might try a hemp-protein based supplement (smoothie) once a day. Hemp protein is probably the best plant-source protein. (the fact that you were 60 pounds overweight on a vegetarian diet makes me wonder how balanced that diet was/is? Watch your intake of processed foods--including 'meat analogs' and dairy products, if you eat them. Both can be calorie dense without being nutrient dense).
Since you are just starting out, you might not notice a lot of difference at first, as the first strength changes come about more through neuro-muscular adaptation (ie: your nervous system learning to recruit more muscle fibers) than from adding extra muscle tissue. Keep with it, be consistant, don't overdo (RECOVERY is very important for muscle growth. Muscles get the stimulus to repair and grow from the workout, but need the recovery time to actually do the growth). It may take some experimentation to see what the ideal combo of work-to-rest is for you.