Question: Would doing pujas, in general, be more beneficial if it's continued for a longer period of time (a month) or during the 4 auspicious periods? Or would doing pujas at a monastery with many lamas and ensure the effectiveness of the puja? Would it be wrong to assume that lay devotees would have to do this (the chanting etc) for the whole life? Let me elaborate further. I read somewhere that due to each individual's karmic debts or affinity, the ability to receive the merits/blessings would result in how much the person can absorb, as lay devotees or ordinary people. As lay people, we have so much negative karma, as compared to lamas, tulkus, Rinpoches as they have had past lives of strong merit bases as compared to lay people.
Answer: Doing puja for certain purpose is usually more beneficial on auspicious days as merits multiply many times on such special days. Also, the puja is more effective if a person with proper motivation request the Sangha community to conduct the puja. This is because the Sangha upholds the Vinaya precepts and thus they can be considered pure. Sutras also mentioned that Sangha "… are the perfect field of Merits". In this way, pujas conducted by Sangha can be much better than any other persons. Thus, merits are greater and with that more effective.
There are many lay practitioners who are good practitioners. It depends on the background of the layperson. Not every layperson is impure. In Tibetan tradition of Buddhism, there are many great masters who are not monks. Yet, they surpassed most monks in terms of spiritual practice and attainments. So it really depends on individual's achievements.