The book "Lighthouses of Liverpool Bay" by John and Diane Robinson has quite a bit of information about the Hoylake lifeboat in chapter 3 (which is mostly about the Hoylake lighthouses). You can usually find a copy on ebay or abebooks. John and Diane Robinson also compiled the information about the lighthouse keepers of Liverpool Bay which is on the ALK website:
As you say, William Bird kept Hoylake Lower from 1819 until his retirement in 1855. Another Bird, Henry, kept Hoylake Lower from 1860 until his death in 1868. If they were related, I have not found the connection (but I haven't really looked). Nor am I aware of any connection between the John Bird that you mention and Liverpool's lighthouse service. Bird was a common name in North Wirral, especially amongst fisherman in Hoylake.
John and Diane write on page 73 "Joseph Bennett seems to have become less active, perhaps through old age, in the years following the Earl Moira incident. By the end of 1825 the whole of the lifeboat service, locally, had become moribund, so a special committee was set up to deal with the problem. After a year a full report was produced. This resulted in a new and improved lifeboat service that operated from all points around Liverpool Bay. Joseph Bennett remained keeper of the Upper Lighthouse until he died in 1828." They don't give a source for this particular statement. But it does suggest that the relationship between the lighthouse and lifeboat probably altered around 1825.
The Merseyside Maritime Museum Archives hold the extensive Mersey Docks and Harbour Board collection (which is incompletely catalogued). Now, the MDHB wasn't established until 1858, so its primary records won't be contemporaneous with the period you're interested in. Nonetheless there may well be information in those archives that touches on your questions.
Prior to 1858, the lighthouses (and I presume, lifeboats) were operated by the city of Liverpool. So you might have some joy from their records; Liverpool Central Library would be a sensible place to start.
Hope this helps.
Thanks Stephen, I'll go to the maritime museum next week and will make a visit to the central library art the same time. Can you tell me what the Earl Moira incident was please? Cheers, Dave
Actually Stephen, I've found it now thanks, there are of course several newspaper articles about the Earl Moira and I've also read Joseph Bennett's log today with his comments on it - interestingly he didn't name the vessel but the date of Aug 9th 1821 was present and I could put 2 and 2 together to fill in the gaps. We also have a sea chart from the early 1900s where we could identify the Gut no.1 buoy and Wharf Bank which aren't on modern day charts.
Thanks for the info, very interesting!