In the UK you can simultaneously have the BA Amex, the Tesco clubcard that gives Avios and the Green/Plat/Cent Amex that give you membership rewards. Can't see why you could not add the Lloyds cards as well (I have not tried).

One potential catch is that the UK cards must be linked to a UK BAEC account so if your Chase card is in the US and linked to a US BAEC address, the Avios may not transfer. In that case, you can still get the Lloyds card but the Avios will accrue and will only be transferred into your account when you change your BAEC to a UK address (you can change your BAEC address every 6 months).