The specific requirements for LAPL holders to upgrade to a PPL are:
FCL.210.A PPL(A) — Experience requirements and crediting
(b) Specific requirements for applicants holding an LAPL(A). Applicants for a PPL(A) holding an LAPL(A) shall have completed at least 15 hours of flight time on aeroplanes after the issue of the LAPL(A), of which at least 10 shall be flight instruction completed in a training course at an ATO. This training course shall include at least 4 hours of supervised solo flight time, including at least 2 hours of solo cross-country flight time with at least 1 cross-country flight of at least 270 km (150 NM), during which full stop landings at 2 aerodromes different from the aerodrome of departure shall be made.
The LAPL(A) has no validity outside EASA states - so you couldn't complete the solo flying in the USA. Which would have to be under the supervision of an FI anyway - and you won't find many ATOs approved for Part-FCL training in the USA before long, due to the prohibitive cost of EASA approval.
The FAA has already rejected 61.75 applications from LAPL(A) holders, due to the licence being sub-ICAO.
Whether the CAA would accept the 15-10=5 other hours of 'flight time on aeroplanes' if it was flown PU/T with a non-EASA FI in the USA, I do not know. But flying over to the USA to fly 5 dual hours seems an expensive way of doing things to me.