I can't see a death for Joan or another marriage for Richard. Perhaps they moved away for a while? The only burials that seem to apply to the immediate family are :
1602 7 Sep Richard s/o Richard LYON
1644 17 Aug Richard LION
*1655 Toby LYON
(this is in the index but I cannot find it anywhere else, it is said to be an inserted entry but I have gone round and round in circles without finding it!Some marriages:
1641 24 Jul Tobias LION & Margreat CURTTIS
1645 18 Aug John LION & Elizabeth ALLEN
Burial of Elizabeth w/o John LION 31 Jan 1649/50 then
1651 Nov 1 John LION & Elizabeth WESTOLL
There are quite a lot of LEWES alias CORVAR (CARVER) entries - this may be the burial of Joan's father:
1580 May 28 Richard LEWES alias CORVAR
and her mother:
1605 Dec 18 Elizabeth LEWES alias CORVAR wid
This may be Joan's baptism:
1577 Dec 13 Joane d/o Richard LEWES alias CORVAR [CARVER]
there is also
1566 Apr 1 Joane d/o John CORVAR [CARVER]
but this would make her a bit old to have John. There is no marriage of a Richard Lewes etc with an Elizabeth to confirm the parentage. But there are burials for 2 Johns, one of whom had a wife Elizabeth who predeceased him. The other John seems to have married an Alice. So on balance I think her father must have been Richard.
* found it - Jan 31 so year is 1655/6. The inserted burials were under marriages, very easy to miss

Joan wasn't there, either.