Lawn bowlers really don’t need a lot of strength. So long as the surface they play on is reasonably fast, the potential energy from allowing the bowl to defend to the rolling surface combined with the kinetic energy from a pendulum swing is sufficient to take a bowl to the full length of the rink.
What lawn bowlers need, increasingly as they get older, is improved balance. Most delivery motions involve a stepping forward with the advancing foot and a brief balancing on the anchor foot. Brief as this is, a partial loss of balance by your entire body can lead to deviations in achieving the desired line and weight for your shot.
If you have been lawn bowling more or less regularly for six years or more, I think I can provide a little test that will demonstrate that your balance may be more important for your delivery than you think.
Take a bowl and stand in your ‘ready’ position for starting your bowling delivery. Now raise your stepping foot slightly off the ground so that all your weight is supported on what would be your anchor leg. Start counting: a thousand and one, a thousand and two, etc. stopping the count when you lose your balance. Now switch the bowl to the other hand and repeat, standing with all your weight supported on what would normally be the leg that steps forward. Again count. Repeat these two a few times. At least for me, I have much longer control of my balance standing on my normal anchor leg. This, I hypothesize, is because my lawn bowling has provided practice balancing on my anchor leg.
Doing this exercise, standing beside the back of a chair that you can reach out to when you lose your balance, you should, with practice, be able to stand alone on either leg for 20 seconds. When you can do this controlling your balance perfectly throughout your bowls delivery will be improved commensurate with whatever improvement you have made using the exercise. Try it!