The only information I can (so far) find on Lichfield 
is as follows, from Christopher WHENT'S excellentt site
www.hoasm.org:

"Henry Lichfield was steward to Lady Cheney at her splendid 'Court-like' house at Toddington, near Luton: 'so I, bestowing the day in your ladyship's necessary businesses, borrowed some hours of the night to bestow upon these my compositions ... yet it pleased your honor with gentle ear to receive them, being presented by the instruments and voices of your own family.' The lady is saluted with charming verses by Christopher Brooke:

Unto that vale-like place of lowly height,
Where joy, peace, love make an harmonious chime,
Where civil sports, music and Court delight
Do run divisions on the hours of time,
Where reigns a lady crowned with highest merits
On whom the muses and the graces wait ..."