Lyndsey was born in St. Sepulchre’s parish, London, though his baptism record no longer survives. His father Miles had migrated there from Dent, in Yorkshire’s West Riding. The family were presumably of humble stock, as Lyndsey acquired a coat of arms only in 1608. Miles died intestate in around 1582, leaving at least two sons, and Lyndsey probably received only a modest inheritance.
In July 1615 the 3rd earl of Dorset tackled his escalating burden of debt by conveying a large part of his estate to trustees, including Lyndsey, (Sir) George Rivers* and Richard Amherst*, who were to sell properties or otherwise raise funds to satisfy the earl’s creditors. This complex and daunting task was to occupy Lyndsey for the rest of his life. Dorset failed to rein in his expenditure, and periodically recovered lands from the trustees, thereby undermining their efforts. One loan of about £14,000, taken out in 1618 and scheduled for repayment over five years, was renegotiated in 1621 with barely any reduction in the sum owing to the lender. By early 1624 Lyndsey’s instructions as a trustee had been modified four times to accommodate the earl’s changing needs, and he was also involved in the financial affairs of Dorset’s brother and heir, Sir Edward Sackville*.
Lyndsey was probably already leasing land at Hailsham, Sussex by 1617, which may explain his appointment in that year to a sewers commission within the county. During the next decade he accumulated several hundred acres of land in the Hailsham district, some of it from his master, while in 1621 he purchased a country seat at nearby Buxted. In this latter transaction he again seems to have taken advantage of the previous owner’s financial difficulties, though the Buxted estate came to him encumbered with certain annuities which Lyndsey was unable to cancel, despite bringing a suit in Chancery.
In January 1626 Lyndsey was elected to Parliament at Camelford. Since his fellow Sackville servant, Evan Edwards, also secured a seat there in 1628, it appears that he relied on the backing of the 4th earl of Dorset. Although Dorset lacked direct ties with the borough, one of his long-standing colleagues on the Middlesex bench was Sir Robert Killigrew*, who owned property near Camelford. On 17 Mar. Lyndsey was nominated to a committee to scrutinize a private bill concerning Dorset’s cousin, Sir Thomas Neville. He was also added to the committee dealing with the Bave and Sotherne naturalization bill, and attended at least one meeting, though it is unclear why he took an interest in this measure.
By this time Lyndsey was increasingly treating Buxted as his main home, and although he never became an active member of the Sussex bench he was appointed to several important local commissions in the later 1620s. He and his fellow trustees made slow but steady progress with settling the Dorset debts, for example reducing the burden by £8,000 between mid-1628 and mid-1629.