Before we get to law firms, some factors to consider first:
Which market are we talking about? What are the causes of this recession? What sectors are these impacting? In what circumstances will a recession impact law firms? What law firms are we talking about?
It's pretty hard to generalise and say 'law firms will be impacted by a recession' because it depends on so many factors.
If you want to think about the general impact, it can help to start from the basics. Law firms will be impacted if they're making less money and/or their costs are going up. It could be the case that a recession impacts their revenue if clients are spending less on legal services (e.g. due to a fall in demand or because they're putting pressure on fees). The question is whether that is actually happening in the market. Are clients actually spending less on legal services? Are they doing fewer deals? For example, if we're talking about the UK, you might consider how Brexit-related work could offset some of the impact. Or you might consider what kind of work the firm does. If the firm primarily acts for private equity clients, are they still going to be impacted in the same way?
If things get really bad, law firms might need to cut their costs. That could mean restructuring their operations, laying off staff, freezing wages etc. You can learn a lot from what law firms did during the financial crisis.
Law firms can do lots of things to try mitigate the effects. If they have a broad international presence, they'll be less exposed to a slowdown in one market (e.g. if the UK slows down but the US is booming). In times of financial crises, transactional work may slow down (clients don't want to buy other companies or invest until things have improved). Law firms may try to hedge against that risk by investing in countercyclical practice areas: in times of recession, departments like restructuring/insolvency and litigation may see an increase in demand. If clients' legal budgets are being cut, law firms could think about reducing their fees/offering different pricing options/adding value in different ways to win work.
