But, at the same time, low interest rate may mean that lenders may not be very keen on giving out loans. For example, people would find no use in keeping cash into bank accounts which provide low interest rates. This may drive down lending, and hence investment.
This is not entirely true. Bank profitability and willingness to lend depend on intermediation margin. Difference between the deposit or Fed funds interest rate and interest on loans they make.
For example a bank would be much happier to lend at 3% interest rate when federal funds rate or deposit rate is 0% than it would be happy to lend when interest rate is 20% but federal funds rate or deposit rate is 19.5% as they earn more profit at the lower rate with higher intermediation margin.
What low interest does is to discourage supply of saving, although even here the decision depends more on real interest rate than nominal one. Nonetheless, banks could always just get their funds from Fed, so unless Fed decides not to provide ample reserves they could in principle go on lending as much as they want.
If so, why is low n.i.r. considered good for economic growth?
It can actually be considered bad for the growth, but it is because of their effect on market concentration and firm productivity not because of any limits on loans. For example, Liu et al 2022 show that:
a decline in the long-term interest rate can trigger a stronger investment response by market leaders relative to market followers, thereby leading to more concentrated markets, higher profits, and lower aggregate productivity growth. This strategic effect of lower interest rates on market concentration implies that aggregate productivity growth declines as the interest rate approaches zero.
Moreover, Bikker & Vervliet (2017) argue low interest rates promote excessive risk taking which is clearly bad for macroeconomic stability.
Low interest rates can stimulate economic activity in short run, but long run economic growth depends on how fast productivity of different factors is growing.